Chapter 04 - Expectation.ipynb

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   "source": [
    "## 4. Expectation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 Expectation of a Random Variable"
   ]
  },
  {
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   "source": [
    "The **expected value**, **mean** or **first moment** of $X$ is defined to be\n",
    "\n",
    "$$ \\mathbb{E}(X) = \\int x \\; dF(x) = \\begin{cases}\n",
    "\\sum_x x f(x) &\\text{if } X \\text{ is discrete} \\\\\n",
    "\\int x f(x)\\; dx &\\text{if } X \\text{ is continuous}\n",
    "\\end{cases} $$\n",
    "\n",
    "assuming that the sum (or integral) is well-defined.  We use the following notation to denote the expected value of $X$:\n",
    "\n",
    "$$ \\mathbb{E}(X) = \\mathbb{E}X = \\int x\\; dF(x) = \\mu = \\mu_X $$"
   ]
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   "source": [
    "The expectation is a one-number summary of the distribution.  Think of $\\mathbb{E}(X)$ as the average value you'd obtain if you computed the numeric average $n^{-1} \\sum_{i=1}^n X_i$ for a large number of IID draws $X_1, \\dots, X_n$.  The fact that $\\mathbb{E}(X) \\approx n^{-1} \\sum_{i=1}^n X_i$ is a theorem called the law of large numbers which we will discuss later.   We use $\\int x \\; dF(x)$ as a convenient unifying notation between the discrete case $\\sum_x x f(x)$ and the continuous case $\\int x f(x) \\; dx$ but you should be aware that $\\int x \\; dF(x)$ has a precise meaning discussed in real analysis courses.\n",
    "\n",
    "To ensure that $\\mathbb{E}(X)$ is well defined, we say that $\\mathbb{E}(X)$ exists if $\\int_x |x| \\; dF_X(x) < \\infty$.  Otherwise we say that the expectation does not exist.  From now on, wheneverwe discuss expectations, we implicitly assume they exist."
   ]
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   "metadata": {},
   "source": [
    "**Theorem 4.6 (The rule of the lazy statician)**.  Let $Y = r(X)$.  Then\n",
    "\n",
    "$$ \\mathbb{E}(Y) = \\mathbb{E}(r(X)) = \\int r(x) \\; dF_X(x) $$"
   ]
  },
  {
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   "source": [
    "As a special case, let $A$ be an event and let $r(x) = I_A(x)$, where $I_A(x) = 1$ if $x \\in A$ and $I_A(x) = 0$ otherwise.  Then\n",
    "\n",
    "$$ \\mathbb{E}(I_A(X)) = \\int I_A(x) f_X(x) dx = \\int_A f_X(x) dx = \\mathbb{P}(X \\in A) $$\n",
    "\n",
    "In other words, probability is a special case of expectation."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Functions of several variables are handled in a similar way.  If $Z = r(X, Y)$ then\n",
    "\n",
    "$$ \\mathbb{E}(Z) = \\mathbb{E}(r(X, Y)) = \\int \\int r(x, y) \\; dF(x, y) $$\n",
    "\n",
    "The **$k$-th moment** of $X$ is defined to be $\\mathbb{E}(X^k)$, assuming that $\\mathbb{E}(|X|^k) < \\infty$.  We shall rarely make much use of moments beyond $k = 2$."
   ]
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   "source": [
    "### 4.2 Properties of Expectations"
   ]
  },
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   "source": [
    "**Theorem 4.10**.  If $X_1, \\dots, X_n$ are random variables and $a_1, \\dots, a_n$ are constants, then\n",
    "\n",
    "$$ \\mathbb{E}\\left( \\sum_i a_i X_i \\right) = \\sum_i a_i \\mathbb{E}(X_i) $$"
   ]
  },
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   "metadata": {},
   "source": [
    "**Theorem 4.12**.  Let $X_1, \\dots, X_n$ be independent random variables.  Then,\n",
    "\n",
    "$$ \\mathbb{E}\\left(\\prod_i X_i \\right) = \\prod_i \\mathbb{E}(X_i) $$\n",
    "\n",
    "Notice that the summation rule does not require independence but the product does."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 Variance and Covariance"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $X$ be a random variable with mean $\\mu$.  The **variance** of $X$ -- denoted by $\\sigma^2$ or $\\sigma_X^2$ or $\\mathbb{V}(X)$ or $\\mathbb{V}X$ -- is defined by\n",
    "\n",
    "$$ \\sigma^2 = \\mathbb{E}(X - \\mu)^2 = \\int (x - \\mu)^2\\; dF(x) $$\n",
    "\n",
    "assuming this expectation exists.  The **standard deviation** is $\\text{sd}(X) = \\sqrt{\\mathbb{V}(X)}$ and is also denoted by $\\sigma$ and $\\sigma_X$."
   ]
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   "source": [
    "**Theorem 4.14**.  Assuming the variance is well defined, it has the following properties:\n",
    "\n",
    "1.  $\\mathbb{V}(X) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2$\n",
    "2.  If $a$ and $b$ are constants then $\\mathbb{V}(aX + b) = a^2 \\mathbb{V}(X)$\n",
    "3.  If $X_1, \\dots, X_n$ are independent and $a_1, \\dots, a_n$ are constants then\n",
    "\n",
    "    $$ \\mathbb{V}\\left( \\sum_{i=1}^n a_iX_i \\right) = \\sum_{i=1}^n a_i^2 \\mathbb{V}(X_i) $$"
   ]
  },
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   "source": [
    "If $X_1, \\dots, X_n$ are random variables then we define the **sample mean** to be\n",
    "\n",
    "$$ \\overline{X}_n = \\frac{1}{n} \\sum_{i=1}^n X_i  $$\n",
    "\n",
    "and the **sample variance** to be\n",
    "\n",
    "$$ S_n^2 = \\frac{1}{n - 1} \\sum_{i=1}^n \\left(X_i - \\overline{X}_n\\right)^2 $$"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "**Theorem 4.16**.  Let $X_1, \\dots, X_n$ be IID and let $\\mu = \\mathbb{E}(X_i)$, $\\sigma^2 = \\mathbb{V}(X_i)$.  Then\n",
    "\n",
    "$$ \n",
    "\\mathbb{E}\\left(\\overline{X}_n\\right) = \\mu,\n",
    "\\quad\n",
    "\\mathbb{V}\\left(\\overline{X}_n\\right) = \\frac{\\sigma^2}{n},\n",
    "\\quad \\text{and} \\quad\n",
    "\\mathbb{E}\\left(S_n^2\\right) = \\sigma^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If $X$ and $Y$ are random variables, then the covariance and correlation between $X$ and $Y$ measure how strong the linear relationship between $X$ and $Y$ is."
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "Let $X$ and $Y$ be random variables with means $\\mu_X$ and $\\mu_Y$ and standard deviation $\\sigma_X$ and $\\sigma_Y$.  Define the **covariance** between $X$ and $Y$ by\n",
    "\n",
    "$$ \\text{Cov}(X, Y) = \\mathbb{E}[(X - \\mu_X)(Y - \\mu_Y)] $$\n",
    "\n",
    "and the **correlation** by\n",
    "\n",
    "$$ \\rho = \\rho_{X, Y} = \\rho(X, Y) = \\frac{\\text{Cov}(X, Y)}{\\sigma_X \\sigma_Y} $$"
   ]
  },
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   "metadata": {},
   "source": [
    "**Theorem 4.18**.  The covariance satisfies:\n",
    "\n",
    "$$ \\text{Cov}(X, Y) = \\mathbb{E}(XY) - \\mathbb{E}(X) \\mathbb{E}(Y) $$\n",
    "\n",
    "The correlation satisfies:\n",
    "\n",
    "$$ -1 \\leq \\rho(X, Y) \\leq 1 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If $Y = a + bX$ for some constants $a$ and $b$ then $\\rho(X, Y) = 1$ if $b > 0$ and $\\rho(X, Y) = -1$ if $b < 0$.  If $X$ and $Y$ are independent, then $\\text{Cov}(X, Y) = \\rho = 0$.  The converse is not true in general."
   ]
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   "metadata": {},
   "source": [
    "**Theorem 4.19**.\n",
    "\n",
    "$$ \n",
    "\\mathbb{V}(X + Y) = \\mathbb{V}(X) + \\mathbb{V}(Y) + 2 \\text{Cov}(X, Y)\n",
    "\\quad \\text{ and } \\quad\n",
    "\\mathbb{V}(X - Y) = \\mathbb{V}(X) + \\mathbb{V}(Y) - 2 \\text{Cov}(X, Y)\n",
    "$$\n",
    "\n",
    "More generally, for random variables $X_1, \\dots, X_n$,\n",
    "\n",
    "$$ \\mathbb{V}\\left( \\sum_i a_i X_i \\right) = \\sum_i a_i^2 \\mathbb{V}(X_i) + 2 \\sum \\sum_{i < j} a_i a_j \\text{Cov}(X_i, X_j) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4 Expectation and Variance of Important Random Variables"
   ]
  },
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   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{array}{lll}\n",
    "\\text{Distribution} & \\text{Mean} & \\text{Variance}           \\\\\n",
    "\\hline\n",
    "\\text{Point mass at } p      & a             & 0              \\\\\n",
    "\\text{Bernoulli}(p)          & p             & p(1-p)         \\\\\n",
    "\\text{Binomial}(n, p)        & np            & np(1-p)        \\\\\n",
    "\\text{Geometric}(p)          & 1/p           & (1 - p)/p^2    \\\\\n",
    "\\text{Poisson}(\\lambda)      & \\lambda       & \\lambda        \\\\\n",
    "\\text{Uniform}(a, b)         & (a + b) / 2   & (b - a)^2 / 12 \\\\\n",
    "\\text{Normal}(\\mu, \\sigma^2) & \\mu           & \\sigma^2       \\\\\n",
    "\\text{Exponential}(\\beta)    & \\beta         & \\beta^2        \\\\\n",
    "\\text{Gamma}(\\alpha, \\beta)  & \\alpha \\beta  & \\alpha \\beta^2 \\\\\n",
    "\\text{Beta}(\\alpha, \\beta)   & \\alpha / (\\alpha + \\beta) & \\alpha \\beta / ((\\alpha + \\beta)^2 (\\alpha + \\beta + 1)) \\\\\n",
    "t_\\nu                        & 0 \\text{ (if } \\nu > 1 \\text{)} & \\nu / (\\nu - 2) \\text{ (if } \\nu > 2 \\text{)} \\\\\n",
    "\\chi^2_p                     & p             & 2p             \\\\\n",
    "\\text{Multinomial}(n, p)     & np            & \\text{see below} \\\\\n",
    "\\text{Multivariate Nornal}(\\mu, \\Sigma) & \\mu & \\Sigma \\\\\n",
    "\\end{array}\n",
    "$$"
   ]
  },
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   "metadata": {},
   "source": [
    "The last two entries in the table are multivariate models which involve a random vector $X$ of the form\n",
    "\n",
    "$$ X = \\begin{pmatrix} X_1 \\\\ \\vdots \\\\ X_k \\end{pmatrix} $$\n",
    "\n",
    "The mean of a random vector $X$ is defined by\n",
    "\n",
    "$$ \\mu = \\begin{pmatrix} \\mu_1 \\\\ \\vdots \\\\ \\mu_k \\end{pmatrix} = \\begin{pmatrix} \\mathbb{E}(X_1) \\\\ \\vdots \\\\ \\mathbb{E}(X_k) \\end{pmatrix} $$\n",
    "\n",
    "The **variance-covariance matrix** $\\Sigma$ is defined to be\n",
    "\n",
    "$$ \\Sigma = \\begin{pmatrix}\n",
    "\\mathbb{V}(X_1) & \\text{Cov}(X_1, X_2) & \\cdots & \\text{Cov}(X_1, X_k) \\\\\n",
    "\\text{Cov}(X_2, X_1) & \\mathbb{V}(X_2) & \\cdots & \\text{Cov}(X_2, X_k) \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "\\text{Cov}(X_k, X_1) & \\text{Cov}(X_k, X_2) & \\cdots & \\mathbb{V}(X_k)\n",
    "\\end{pmatrix} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If $X \\sim \\text{Multinomial}(n, p)$ then\n",
    "\n",
    "$$ \n",
    "\\mathbb{E}(X) = np = n(p_1, \\dots, p_k)\n",
    "\\quad \\text{and} \\quad\n",
    "\\mathbb{V}(X) = \\begin{pmatrix}\n",
    "np_1(1 - p_1) & -np_1p_2 & \\cdots & -np_1p_k \\\\\n",
    "-np_2p_1 & np_2(1 - p_2) & \\cdots & -np_2p_k \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "-np_kp_1 & -np_kp_2 & \\cdots & np_k(1 - p_k)\n",
    "\\end{pmatrix} $$\n",
    "\n",
    "To see this:\n",
    "\n",
    "- Note that the marginal distribution of any one component is $X_i \\sim \\text{Binomial}(n, p_i)$, so $\\mathbb{E}(X_i) = np_i$ and $\\mathbb{V}(X_i) = np_i(1 - p_i)$.  \n",
    "- Note that, for $i \\neq j$, $X_i + X_j \\sim \\text{Binomial}(n, p_i + p_j)$, so $\\mathbb{V}(X_i + X_j) = n(p_i + p_j)(1 - (p_i + p_j))$.\n",
    "- Using the formula for the covariance of a sum, for $i \\neq j$,\n",
    "\n",
    "$$ \\mathbb{V}(X_i + X_j) = \\mathbb{V}(X_i) + \\mathbb{V}(X_j) + 2 \\text{Cov}(X_i, X_j) =  np_i(1 - p_i) + np_j(1 - p_j) + 2 \\text{Cov}(X_i, X_j) $$\n",
    "\n",
    "Equating the last two formulas we get a formula for the covariance, $\\text{Cov}(X_i, X_j) = -np_ip_j$.\n",
    "\n",
    "Finally, here's a lemma that can be useful for finding means and variances of linear combinations of multivariate random vectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Lemma 4.20**.  If $a$ is a vector and $X$ is a random vector with mean $\\mu$ and variance $\\Sigma$ then\n",
    "\n",
    "$$ \\mathbb{E}(a^T X) = a^T \\mu\n",
    "\\quad \\text{and} \\quad\n",
    "\\mathbb{V}(a^T X) = a^T \\Sigma a $$\n",
    "\n",
    "If $A$ is a matrix then\n",
    "\n",
    "$$ \\mathbb{E}(A X) = A \\mu\n",
    "\\quad \\text{and} \\quad\n",
    "\\mathbb{V}(AX) = A \\Sigma A^T $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.5 Conditional Expectation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The conditional expectation of $X$ given $Y = y$ is\n",
    "\n",
    "$$ \\mathbb{E}(X | Y = y) = \\begin{cases}\n",
    "\\sum x f_{X | Y}(x | y) &\\text{ discrete case} \\\\\n",
    "\\int x f_{X | Y}(x | y) dy &\\text{ continuous case}\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "If $r$ is a function of $x$ and $y$ then\n",
    "\n",
    "$$ \\mathbb{E}(r(X, Y) | Y = y) = \\begin{cases}\n",
    "\\sum r(x, y) f_{X | Y}(x | y) &\\text{ discrete case} \\\\\n",
    "\\int r(x, y) f_{X | Y}(x | y) dy &\\text{ continuous case}\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While $\\mathbb{E}(X)$ is a number, $\\mathbb{E}(X | Y = y)$ is a function of $y$.  Before we observe $Y$, we don't know the value of $\\mathbb{E}(X | Y = y)$ so it is a random variable which we denote $\\mathbb{E}(X | Y)$.  In other words, $\\mathbb{E}(X | Y)$ is the random variable whose value is $\\mathbb{E}(X | Y = y)$ when $Y$ is observed as $y$.  Similarly, $\\mathbb{E}(r(X, Y) | Y)$ is the random variable whose value is $\\mathbb{E}(r(X, Y) | Y = y)$ when $Y$ is observed as $y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Theorem 4.23 (The rule of iterated expectations)**.  For random variables $X$ and $Y$, assuming the expectations exist, we have that\n",
    "\n",
    "$$ \\mathbb{E}[\\mathbb{E}(Y | X)] = \\mathbb{E}(Y)\n",
    "\\quad \\text{and} \\quad\n",
    "\\mathbb{E}[\\mathbb{E}(X | Y)] = \\mathbb{E}(X) $$\n",
    "\n",
    "More generally, for any function $r(x, y)$ we have\n",
    "\n",
    "$$ \\mathbb{E}[\\mathbb{E}(r(X, Y) | X)] = \\mathbb{E}(r(X, Y))\n",
    "\\quad \\text{and} \\quad\n",
    "\\mathbb{E}[\\mathbb{E}(r(X, Y) | Y)] = \\mathbb{E}(r(X, Y)) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Proof**.  We will prove the first equation.\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\mathbb{E}[\\mathbb{E}(Y | X)] &= \\int \\mathbb{E}(Y | X = x) f_X(x) dx = \\int \\int y f(y | x) dy f(x) dx \\\\\n",
    "&= \\int \\int y f(y|x) f(x) dx dy = \\int \\int y f(x, y) dx dy = \\mathbb{E}(Y)\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **conditional variance** is defined as\n",
    "\n",
    "$$ \\mathbb{V}(Y | X = x) = \\int (y - \\mu(x))^2 f(y | x) dx $$\n",
    "\n",
    "where $\\mu(x) = \\mathbb{E}(Y | X = x)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Theorem 4.26**.  For random variables $X$ and $Y$,\n",
    "\n",
    "$$ \\mathbb{V}(Y) = \\mathbb{E}\\mathbb{V}(Y | X) + \\mathbb{V} \\mathbb{E} (Y | X)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.6 Technical Appendix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4.6.1 Expectation as an Integral"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The integral of a measurable function $r(x)$ is defined as follows.  First suppose that $r$ is simple, meaning that it takes finitely many values $a_1, \\dots, a_k$ over a partition $A_1, \\dots, A_k$.  Then  $\\int r(x) dF(x) = \\sum_{i=1}^k a_i \\mathbb{P}(r(X) \\in A_i)$.  The integral of a positive measurable function $r$ is defined by $\\int r(x) dF(x) = \\lim_i \\int r_i(x) dF(x)$, where $r_i$ is a sequence of simple functions such that $r_i(x) \\leq r(x)$ and $r_i(x) \\rightarrow r(x)$ as $i \\rightarrow \\infty$.  This does not depend on the particular sequence.  The integral of a measurable function $r$ is defined to be $\\int r(x) dF(x) = \\int r^+(x) dF(x) - \\int r^-(x) dF(x)$ assuming both integrals are finite, where $r^+(x) = \\max \\{ r(x), 0 \\}$ and $r^-(x) = \\min\\{ r(x), 0 \\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4.6.2  Moment Generating Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **moment generating function (mgf)** or **Laplace transform** of $X$ is defined by\n",
    "\n",
    "$$ \\psi_X(t) = \\mathbb{E}(e^{tX}) = \\int e^{tx} dF(x) $$\n",
    "\n",
    "where $t$ varies over the real numbers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In what follows, we assume the mgf is well defined for all $t$ in small neighborhood of 0.  A related function is the characteristic function, defined by $\\mathbb{E}(e^{itX})$ where $i = \\sqrt{-1}$.  This function is always defined for all $t$.  The mgf is useful for several reasons.  First, it helps us compute the moments of a distribution.  Second, it helps us find the distribution of sums of random variables.  Third, it is used to prove the central limit theorem.\n",
    "\n",
    "When the mgf is well defined, it can be shown that we can interchange the operations of differentiation and \"taking expectation\".  This leads to\n",
    "\n",
    "$$ \\psi'(0) = \\left[ \\frac{d}{dt} \\mathbb{E} e^{tX} \\right]_{t = 0} = \\mathbb{E} \\left[ \\frac{d}{dt} e^{tX} \\right]_{t = 0}\n",
    "= \\mathbb{E}[X e^{tX}]_{t = 0} = \\mathbb{E}(X)\n",
    "$$\n",
    "\n",
    "By taking further derivatives we conclude that $\\psi^{(k)}(0) = \\mathbb{E}(X^k)$.  This gives us a method for computing the moments of a distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Lemma 4.30**.  Properties of the mgf.\n",
    "\n",
    "1.  If $Y = aX + b$ then $\\psi_Y(t) = e^{bt} \\psi_X(at) $\n",
    "2.  if $X_1, \\dots, X_n$ are independent and $Y = \\sum_i X_i$ then $\\psi_Y(t) = \\prod_i \\psi_{i}(t)$, where $\\psi_i$ is the mgf of $X_i$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Theorem 4.32**.  Let $X$ and $Y$ be random variables.  If $\\psi_X(t) = \\psi_Y(t)$ for all $t$ in an open interval around 0, then $X \\overset{d}= Y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Moment Generating Function for Some Common Distributions**\n",
    "\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "\\text{Distribution} & \\text{mgf} \\\\\n",
    "\\hline\n",
    "\\text{Bernoulli}(p)   & pe^t + (1 - p)         \\\\\n",
    "\\text{Binomial}(n, p) & (pe^t + (1 - p))^n     \\\\\n",
    "\\text{Poisson}(\\lambda) & e^{\\lambda(e^t - 1)} \\\\\n",
    "\\text{Normal}(\\mu, \\sigma^2) & \\exp\\left\\{\\mu t + \\frac{\\sigma^2 t^2}{2} \\right\\} \\\\\n",
    "\\text{Gamma}(\\alpha, \\beta) & \\left( \\frac{\\beta}{\\beta - t} \\right)^\\alpha \\text{ for } t < \\beta\n",
    "\\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.7 Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.1**.  Suppose we play a game where we start with $c$ dollars.  On each play of the game you either double your money or half your money, with equal probability.  What is your expected fortune after $n$ trials?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  Let the random variables $X_i$ be the fortune after the $i$-th trial, $X_0 = c$ always taking the value $c$.  Then:\n",
    "\n",
    "$$ \\mathbb{E}[X_{i + 1} | X_i = x] = 2x \\cdot \\frac{1}{2} + \\frac{x}{2} \\cdot \\frac{1}{2} = \\frac{5}{4}x $$\n",
    "\n",
    "Taking the expectation on $X_i$ on both sides (i.e. integrating over $F_{X_i}(x)$),\n",
    "\n",
    "$$ \\mathbb{E}(\\mathbb{E}[X_{i + 1} | X_i = x]) = \\frac{5}{4} \\mathbb{E}(X_i) \\Longrightarrow \\mathbb{E}(X_{i+1}) = \\frac{5}{4}  \\mathbb{E}(X_i)$$\n",
    "\n",
    "Therefore, by induction,\n",
    "\n",
    "$$ \\mathbb{E}(X_n) = \\left(\\frac{5}{4}\\right)^n c $$\n",
    "\n",
    "Note that this is **not** a martingale, as in the traditional double-or-nothing formulation -- the expected value goes up at each iteration."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.2**.  Show that $\\mathbb{V}(X) = 0$ if and only if there is a constant $c$ such that $\\mathbb{P}(X = c) = 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  We have $\\mathbb{V}(X) = \\mathbb{E}[(X - \\mathbb{E}(X))^2]$:\n",
    "\n",
    "$$ \\mathbb{V}(X) = \\int (x - \\mu_X)^2 dF_X(x) $$\n",
    "\n",
    "Since $(x - \\mu_X)^2 \\geq 0$, in order for the variance to be 0 we must have the integrand be zero with probability 1, i.e. $\\mathbb{P}(X = \\mu_X) = 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.3**.  Let $X_1, \\dots, X_n \\sim \\text{Uniform}(0, 1)$ and let $Y_n = \\max \\{ X_1, \\dots, X_n \\}$.  Find $\\mathbb{E}(Y_n)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  The CDF of $Y_n$, for $0 \\leq y \\leq 1$, is:\n",
    "\n",
    "$$ F_{Y_n}(y) = \\mathbb{P}(Y_n \\leq y) = \\prod_{i=1}^n \\mathbb{P}(X_i \\leq y) = y^n $$\n",
    "\n",
    "so its PDF is $f_{Y_n}(y) = F'_{Y_n}(y) = n y^{n-1}$ for $0 \\leq y \\leq 1$.\n",
    "\n",
    "The expected value of $Y_n$ then is\n",
    "\n",
    "$$ \\mathbb{E}(Y_n) = \\int_0^1 y f_{Y_n}(y) dy = \\int_0^1 n y^n dy = \\frac{n}{n+1} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.4**.  A particle starts at the origin of the real line and moves along the line in jumps of one unit.  For each jump the probability is $p$ that the particle will move one unit to the left and the probability is $1 - p$ that the particle will jump one unit to the right.  Let $X_n$ be the position of the particle after $n$ units.  Find $\\mathbb{E}(X_n)$ and $\\mathbb{V}(X_n)$.  (This is known as a random walk.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  \n",
    "\n",
    "We can define $X_n = \\sum_{i=1}^n (1 - 2Y_i)$, where $Y_i \\sim \\text{Bernoulli}(p)$ and the $Y_i$'s are independent random variables representing the direction of each jump.\n",
    "\n",
    "We then have:\n",
    "\n",
    "$$ \\mathbb{E}(X_n) = \\sum_{i=1}^n \\mathbb{E}(1 - 2Y_i) = \\sum_{i=1}^n (1 - 2p) = n(1 - 2p) $$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\mathbb{V}(X_n) = \\sum_{i=1}^n \\mathbb{V}(1 - 2Y_i) \\sum_{i=1}^n 4\\mathbb{V}(Y_i) = 4np(1 - p) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.5**.  A fair coin is tossed until a head is obtained.  What is the expected number of tosses that will be required?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  The number of tosses follows a geometric distribution, $X \\sim \\text{Geom}(p)$, where $p$ is the probability of heads.  Let's deduce its expected value, rather than use it as a known fact ($\\mathbb{E}(X) = 1/p$).  The PDF is\n",
    "\n",
    "$$ f_X(k) = p (1 - p)^{k - 1}, \\quad k > 0 $$\n",
    "\n",
    "The expected value for $X$ is\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\mathbb{E}(X) &= \\sum_{k=1}^\\infty k p (1 - p)^{k - 1}  \\\\\n",
    "&= \\sum_{k=1}^\\infty p(1-p)^{k-1} + \\sum_{k=2}^\\infty (k - 1) p(1-p)^{k - 1} \\\\\n",
    "&= p \\left( 1 + (1 - p) + (1 - p)^2 + \\dots \\right) + \\sum_{k=1}^\\infty k p(1-p)^k \\\\\n",
    "&= p \\left(\\frac{1}{1 - (1 - p)}\\right) + (1 - p) \\sum_{k=1}^\\infty k p(1-p)^{k - 1} \\\\\n",
    "&= 1 + (1 - p) \\mathbb{E}(X)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "from where we get $\\mathbb{E}(X) = 1 / p$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.6**.  Prove Theorem 4.6 for discrete random variables.\n",
    "\n",
    "Let $Y = r(X)$.  Then\n",
    "\n",
    "$$ \\mathbb{E}(Y) = \\mathbb{E}(r(X)) = \\int r(x) \\; dF_X(x) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  The result is immediate from the definition of expectation:\n",
    "\n",
    "$$ Y(\\omega) = r(X(\\omega)) = r(x) \\quad \\forall \\omega : X(\\omega) = x $$\n",
    "\n",
    "and so\n",
    "\n",
    "$$ \\mathbb{E}(Y) = \\int r(x) dF_x(x) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.7**.  Let $X$ be a continuous random variable with CDF $F$.  Suppose that $\\mathbb{P}(X > 0) = 1$ and that $\\mathbb{E}(X)$ exists.  Show that $\\mathbb{E}(X) = \\int_0^\\infty \\mathbb{P}(X > x) dx$.\n",
    "\n",
    "Hint: Consider integrating by parts.  The following fact is helpful: if $\\mathbb{E}(X)$ exists then $\\lim_{x \\rightarrow +\\infty} x | 1 - F(x) | = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  Let's prove the following, slightly more general, lemma.\n",
    "\n",
    "Lemma:  For every continuous random variable $X$,\n",
    "\n",
    "$$ \\mathbb{E}(X) = \\int_0^\\infty (1 - F_X(y)) dy - \\int_{-\\infty}^0 F_X(y) dy $$\n",
    "\n",
    "Proof:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\mathbb{E}(X) &= \\int_{-\\infty}^\\infty x f_X(x) dx \\\\\n",
    "&= \\int_{-\\infty}^0 \\int_x^0 -f_X(x) dy dx + \\int_0^\\infty \\int_0^x f_X(x) dy dx \\\\\n",
    "&= -\\int_{-\\infty}^0 \\int_{-\\infty}^y f_X(x) dx dy + \\int_0^\\infty \\int_y^\\infty f_X(x) dx dy \\\\\n",
    "&= -\\int_{\\infty}^0 \\mathbb{P}(X \\leq y) dy + \\int_0^\\infty \\mathbb{P}(X \\geq y) dy \\\\\n",
    "&= \\int_0^\\infty (1 - F_X(y)) dy - \\int_{-\\infty}^0 F_X(y) dy\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "The result follows by imposing $\\mathbb{P}(X > 0) = 1$, which implies $\\int_{-\\infty}^0 F_X(y) dy = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.8**.  Prove Theorem 4.16.\n",
    "\n",
    "Let $X_1, \\dots, X_n$ be IID and let $\\mu = \\mathbb{E}(X_i)$, $\\sigma^2 = \\mathbb{V}(X_i)$.  Then\n",
    "\n",
    "$$ \n",
    "\\mathbb{E}\\left(\\overline{X}_n\\right) = \\mu,\n",
    "\\quad\n",
    "\\mathbb{V}\\left(\\overline{X}_n\\right) = \\frac{\\sigma^2}{n},\n",
    "\\quad \\text{and} \\quad\n",
    "\\mathbb{E}\\left(S_n^2\\right) = \\sigma^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.\n",
    "\n",
    "For the expected value of sample mean:\n",
    "\n",
    "$$ \\mathbb{E}\\left(\\overline{X}_n\\right) \n",
    "= \\mathbb{E}\\left( \\frac{1}{n} \\sum_{i=1}^n X_i \\right)\n",
    "= \\frac{1}{n} \\sum_{i=1}^n \\mathbb{E}(X_i)\n",
    "= \\frac{1}{n} n\\mu = \\mu $$\n",
    "\n",
    "For the variance of sample mean:\n",
    "\n",
    "$$ \\mathbb{V}\\left(\\overline{X}_n\\right) \n",
    "= \\mathbb{V}\\left( \\frac{1}{n} \\sum_{i=1}^n X_i \\right)\n",
    "= \\frac{1}{n^2} \\sum_{i=1}^n \\mathbb{V}(X_i)\n",
    "= \\frac{1}{n^2} n \\sigma^2 = \\frac{\\sigma^2}{n} $$\n",
    "\n",
    "For the expected value of sample variance:\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\mathbb{E}(S_n^2) &= \\mathbb{E}\\left(\\frac{1}{n - 1} \\sum_{i=1}^n \\left(X_i - \\overline{X}_n\\right)^2 \\right) \\\\\n",
    "&= \\frac{1}{n - 1} \\mathbb{E} \\left( \\sum_{i=1}^n \\left(X_i - \\overline{X}_n\\right)^2 \\right) \\\\\n",
    "&= \\frac{1}{n - 1} \\mathbb{E} \\left( \\sum_{i=1}^n X_i^2 - 2 X_i \\overline{X}_n + \\overline{X}_n^2 \\right) \\\\\n",
    "&= \\frac{1}{n - 1} \\mathbb{E} \\left( \\sum_{i=1}^n X_i^2 - 2 \\overline{X}_n \\sum_{i=1}^n X_i + n \\overline{X}_n^2 \\right) \\\\\n",
    "&= \\frac{1}{n - 1} \\mathbb{E} \\left( \\sum_{i=1}^n X_i^2 - 2 \\overline{X}_n \\cdot n \\overline{X}_n  + n \\overline{X}_n^2 \\right) \\\\\n",
    "&= \\frac{1}{n - 1} \\mathbb{E} \\left( \\sum_{i=1}^n X_i^2 - n \\overline{X}_n^2 \\right) \\\\\n",
    "&= \\frac{1}{n - 1} \\left( \\sum_{i=1}^n  \\mathbb{E}(X_i^2) - n \\mathbb{E}\\left( \\overline{X}_n^2 \\right) \\right) \\\\\n",
    "&= \\frac{1}{n - 1} \\left( \\sum_{i=1}^n \\left(\\mathbb{V}(X_i) + \\mathbb{E}(X_i)^2 \\right) - n \\left(\\mathbb{V}\\left( \\overline{X}_n \\right) + \\mathbb{E}\\left(\\overline{X}_n\\right)^2 \\right)\\right) \\\\\n",
    "&= \\frac{1}{n -1} \\left( n \\left( \\sigma^2 + \\mu^2\\right) - n \\left(\\frac{\\sigma^2}{n} + \\mu^2 \\right) \\right) \\\\\n",
    "&= \\sigma^2\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.9 (Computer Experiment)**.  Let $X_1, \\dots, X_n$ be $N(0, 1)$ random variables and let $\\overline{X}_n = n^{-1} \\sum_{i=1}^n X_i$.  Plot $\\overline{X}_n$ versus $n$ for $n = 1, \\dots, 10,000$.  Repeat for $X_1, \\dots, X_n \\sim \\text{Cauchy}$.  Explain why there is such a difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import norm, cauchy\n",
    "\n",
    "np.random.seed(0)\n",
    "\n",
    "N = 10000\n",
    "X = norm.rvs(size=N)\n",
    "Y = cauchy.rvs(size = N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "nn = np.arange(1, N + 1)\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "\n",
    "ax = plt.subplot(2, 1, 1)\n",
    "ax.plot(nn, np.cumsum(X) / nn)\n",
    "ax.set_title('N(0, 1)')\n",
    "ax.set_xlabel('n')\n",
    "ax.set_ylabel(r'$\\overline{X}_n$')\n",
    "\n",
    "ax = plt.subplot(2, 1, 2)\n",
    "ax.plot(nn, np.cumsum(Y) / nn)\n",
    "ax.set_title('Cauchy')\n",
    "ax.set_xlabel('n')\n",
    "ax.set_ylabel(r'$\\overline{X}_n$')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean on the Cauchy distribution is famously undefined: $\\overline{X}_ n$ is not going to converge."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.10**.  Let $X \\sim N(0, 1)$ and let $Y = e^X$.  Find $\\mathbb{E}(Y)$ and $\\mathbb{V}(Y)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.\n",
    "\n",
    "The CDF of $Y$ is, for $y > 0$:\n",
    "\n",
    "$$ F_Y(y) = \\mathbb{P}(Y \\leq y) = \\mathbb{P}(X \\leq \\log y) = \\Phi(\\log y) $$\n",
    "\n",
    "and so the PDF is\n",
    "\n",
    "$$ f_Y(y) = F'_Y(y) = \\frac{d}{dy} \\Phi(\\log y) = \\frac{d \\Phi(\\log y)}{d \\log y} \\frac{d \\log y}{dy} = \\frac{\\phi(\\log y)}{y}$$\n",
    "\n",
    "The expected value is\n",
    "\n",
    "$$ \\mathbb{E}(Y) = \\int y f_Y(y) dy = \\int_0^\\infty y \\frac{\\phi(\\log y)}{y} dy = \\int_0^\\infty \\phi(\\log y)\\; dy = \\sqrt{e}$$\n",
    "\n",
    "The expected value of $Y^2$ is\n",
    "\n",
    "$$ \\mathbb{E}(Y^2) = \\int y^2 f_Y(y) dy = \\int_0^\\infty y^2 \\frac{\\phi(\\log y)}{y} dy = \\int_0^\\infty y \\phi(\\log y)\\; dy = e^2$$\n",
    "\n",
    "and so the variance is\n",
    "\n",
    "$$ \\mathbb{V}(Y) = \\mathbb{E}(Y^2) - \\mathbb{E}(Y)^2 = e(e - 1) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.11  (Computer Experiment: Simulating the Stock Market)**.  Let $Y_1, Y_2, \\dots$ be independent random variables such that $\\mathbb{P}(Y_i = 1) = \\mathbb{P}(Y_i = -1) = 1/2$.  Let $X_n = \\sum_{i=1}^n Y_i$.  Think of $Y_i = 1$ as \"the stock price increased by one dollar\" $Y_i = -1$ as \"the stock price decreased by one dollar\" and $X_n$ as the value of the stock on day $n$.\n",
    "\n",
    "**(a)**  Find $\\mathbb{E}(X_n)$ and $\\mathbb{V}(X_n)$.\n",
    "\n",
    "**(b)**  Simulate $X_n$ and plot $X_n$ versus $n$ for $n = 1, 2, \\dots, 10,000$.  Repeat the whole simulation several times.  Notice two things.  First, it's easy to \"see\" patterns in the sequence even though it is random.  Second, you will find that the runs look very different even though they were generated the same way.  How do the calculations in (a) explain the second observation?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.\n",
    "\n",
    "**(a)**  We have:\n",
    "\n",
    "$$ \\mathbb{E}(X_n) = \\mathbb{E}\\left( \\sum_{i=1}^n Y_i \\right) = \\sum_{i=1}^n \\mathbb{E}(Y_i) = 0 $$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\mathbb{E}(X_n^2) &= \\mathbb{E}\\left( \\left( \\sum_{i=1}^n Y_i \\right)^2 \\right) \\\\\n",
    "&= \\mathbb{E}\\left( \\sum_{i=1}^n Y_i^2 + \\sum_{i=1}^n \\sum_{j = 1, j \\neq i}^n Y_i Y_j \\right) \\\\\n",
    "&= \\sum_{i=1}^n \\mathbb{E}(Y_i^2) + \\sum_{i=1}^n \\sum_{j = 1, j \\neq i}^n \\mathbb{E}(Y_i Y_j) \\\\\n",
    "&= \\sum_{i=1}^n 1 + \\sum_{i=1}^n \\sum_{j = 1, j \\neq i}^n 0 \\\\\n",
    "&= n\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "so \n",
    "\n",
    "$$\\mathbb{V}(X_n) = \\mathbb{E}(X_n^2) - \\mathbb{E}(X_n)^2 = n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(b)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import norm, bernoulli\n",
    "\n",
    "N = 10000\n",
    "B = 20\n",
    "\n",
    "Y = 2 * bernoulli.rvs(p=1/2, loc=0, size=(B, N), random_state=0) - 1\n",
    "X = np.cumsum(Y, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "\n",
    "nn = np.arange(1, N + 1)\n",
    "\n",
    "z = norm.ppf(0.975)\n",
    "plt.plot(nn, z * np.sqrt(nn), color='red')\n",
    "plt.plot(nn, -z * np.sqrt(nn), color='red')\n",
    "plt.fill_between(nn, z * np.sqrt(nn), -z * np.sqrt(nn), color='red', alpha=0.05)\n",
    "\n",
    "for b in range(B):\n",
    "    plt.plot(nn, X[b])\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standard deviation is $\\sqrt{n}$ -- it scales up with the square root of the \"time\".  The plot above draws $z_{\\alpha / 2} \\sqrt{n}$ curves -- confidence bands for $1 - \\alpha = 95\\%$ -- that contain most of the randomly generated path."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.12**.  Prove the formulas given in the table at the beginning of Section 4.4 for the Bernoulli, Poisson, Uniform, Exponential, Gamma, and Beta.  Here are some hints.  For the mean of the Poisson, use the fact that $e^a = \\sum_{x=0}^a a^x / x!$.  To compute the variance, first compute $\\mathbb{E}(X(X - 1))$.  For the mean of the Gamma, it will help to multiply and divide by $\\Gamma(\\alpha + 1) / \\beta^{\\alpha + 1}$ and use the fact that a Gamma density integrates to 1.  For the Beta, multiply and divide by $\\Gamma(\\alpha + 1) \\Gamma(\\beta) / \\Gamma(\\alpha + \\beta + 1)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.\n",
    "\n",
    "We will do all expressions in the table instead (other than multinomial and multivariate normal, where proofs are already provided in the book)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Point mass at $p$**.  Let $X$ have a point mass at $p$.  Then:\n",
    "\n",
    "- $\\mathbb{E}(X) = p \\cdot 1 = p$\n",
    "- $\\mathbb{E}(X^2) = p^2 \\cdot 1 = p^2$\n",
    "- $\\mathbb{V}(X) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2 = p^2 - p^2 = 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Bernoulli**.  Let $X \\sim \\text{Bernoulli}(p)$.  Then:\n",
    "\n",
    "- $\\mathbb{E}(X) = 1 \\cdot p + 0 \\cdot (1 - p) = p $\n",
    "- $\\mathbb{E}(X^2) = 1 \\cdot p + 0 \\cdot (1 - p) = p$\n",
    "- $\\mathbb{V}(X^2) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2 = p(1 - p)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Binomial**.  Let $X \\sim \\text{Binomial}(n, p)$.  Then $X = \\sum_{i=1}^n Y_i$, where $Y_i \\sim \\text{Bernoulli}(p)$ are IID random variables.\n",
    "\n",
    "- $\\mathbb{E}(X) = \\mathbb{E}\\left( \\sum_{i=1}^n Y_i \\right) = \\sum_{i=1}^n \\mathbb{E}(Y_i) = np $\n",
    "- $\\mathbb{V}(X) = \\mathbb{V}\\left(\\sum_{i=1}^n Y_i \\right) = \\sum_{i=1}^n \\mathbb{V}(Y_i) = np(1-p) $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Geometric**.  Let $X \\sim \\text{Geometric}(p)$.  Then:\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\mathbb{E}(X) &= \\sum_{k=1}^\\infty k p (1 - p)^{k - 1}  \\\\\n",
    "&= \\sum_{k=1}^\\infty p(1-p)^{k-1} + \\sum_{k=2}^\\infty (k - 1) p(1-p)^{k - 1} \\\\\n",
    "&= p \\left( 1 + (1 - p) + (1 - p)^2 + \\dots \\right) + \\sum_{k=1}^\\infty k p(1-p)^k \\\\\n",
    "&= p \\left(\\frac{1}{1 - (1 - p)}\\right) + (1 - p) \\sum_{k=1}^\\infty k p(1-p)^{k - 1} \\\\\n",
    "&= 1 + (1 - p) \\mathbb{E}(X)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Solving for the expectation, we get $\\mathbb{E}(X) = 1/p$.\n",
    "\n",
    "We also have:\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\mathbb{E}(X^2) &= \\sum_{k=1}^\\infty k^2 p (1 - p)^{k - 1}  \\\\\n",
    "&= \\sum_{k=1}^\\infty k p(1-p)^{k-1} + \\sum_{k=2}^\\infty (k^2 - k) p(1-p)^{k - 1} \\\\\n",
    "&= \\mathbb{E}(X) + (1 - p) \\sum_{k=1}^\\infty (k^2 + k) p(1-p)^{k - 1} \\\\\n",
    "&= \\mathbb{E}(X) + (1 - p) \\mathbb{E}(X) + (1 - p) \\sum_{k=1}^\\infty k^2 p(1-p)^{k-1} \\\\\n",
    "&= \\frac{2 - p}{p} + (1 - p) \\mathbb{E}(X^2)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Solving for the expectation, we get $\\mathbb{E}(X^2) = (2 - p) / p^2$.\n",
    "\n",
    "Finally,\n",
    "\n",
    "$$ \\mathbb{V}(X) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2 = \\frac{2 - p}{p^2} - \\frac{1}{p^2} = \\frac{1 - p}{p^2} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Poisson**.  Let $X \\sim \\text{Poisson}(\\lambda)$.  Then:\n",
    "\n",
    "- $ \\mathbb{E}(X) = \\sum_{k=0}^\\infty k \\frac{\\lambda^k e^{-\\lambda}}{k!} = \\lambda e^{-\\lambda} \\sum_{k=1}^\\infty \\frac{\\lambda^{k - 1} }{(k - 1)!} = \\lambda e^{-\\lambda} \\sum_{k=0}^\\infty \\frac{\\lambda^k}{k!} = \\lambda e^{-\\lambda} e^{\\lambda} = \\lambda $\n",
    "\n",
    "- $ \\mathbb{E}(X^2) = \\sum_{k=0}^\\infty k^2 \\frac{\\lambda^k e^{-\\lambda}}{k!} = \\lambda \\sum_{k=1}^\\infty k \\frac{\\lambda^{k-1} e^{-\\lambda} }{(k-1)!} = \\lambda \\sum_{k=0}^\\infty (k + 1) \\frac{\\lambda^{k} e^{-\\lambda} }{k!} = \\lambda \\mathbb{E}(X + 1) = \\lambda(\\lambda + 1) $\n",
    "\n",
    "- $ \\mathbb{V}(X) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2 = \\lambda^2 + \\lambda - \\lambda^2 = \\lambda $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Uniform**.  Let $X \\sim \\text{Uniform}(a, b)$.  Then:\n",
    "\n",
    "- $\\mathbb{E}(X) = \\int_a^b x \\frac{1}{b - a} dx = \\frac{a + b}{2}$\n",
    "- $\\mathbb{E}(X^2) = \\int_a^b x^2 \\frac{1}{b - a} dx = \\frac{a^2 + ab + b}{3}$\n",
    "- $\\mathbb{V}(X) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2 = \\frac{a^2 + ab + b}{3} - \\frac{a^2 + 2ab + b^2}{4} = \\frac{(b - a)^2}{12}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Normal**.  Let $X \\sim N(\\mu, \\sigma^2)$.  Converting into a standard normal, we get $Z = (X - \\mu) / \\sigma \\sim N(0, 1)$.  Then:\n",
    "\n",
    "- $ \\mathbb{E}(X) = \\mathbb{E}(\\sigma Z + \\mu) = \\sigma \\mathbb{E}(Z) + \\mu = \\mu$\n",
    "- $ \\mathbb{V}(X) = \\mathbb{V}(\\sigma Z + \\mu) = \\sigma^2 \\mathbb{V}(Z) = \\sigma^2$\n",
    "\n",
    "To prove that the expected value $Z$ is 0, note that the PDF of $Z$ is even, $\\phi(z) = \\phi(-z)$, so\n",
    "\n",
    "$$ \\mathbb{E}(Z) = \\int_{-\\infty}^\\infty z \\phi(z) dz = \\int_{-\\infty}^0 z \\phi(z) dz + \\int_0^\\infty z \\phi(z) dz = \n",
    "\\int_0^\\infty -z \\phi(-z) dz + \\int_0^\\infty z \\phi(z) dz = \\int_0^\\infty (-z + z)\\phi(z) = 0 $$\n",
    "\n",
    "To prove that the variance of $Z$ is 0, write out the integral explicitly for the expectation of $Z^2$,\n",
    "\n",
    "$$ \\mathbb{E}(Z^2) = \\int_{-\\infty}^\\infty z^2 \\phi(z) dz = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^\\infty z^2 e^{-z^2/2} dz\n",
    "= \\left[ \\Phi(z) - \\frac{1}{\\sqrt{2 \\pi}}  z e^{-z^2/2} \\right]_{-\\infty}^\\infty = \\lim_{x \\rightarrow +\\infty} \\Phi(x) - \\lim_{x \\rightarrow -\\infty} \\Phi(x) = 1 - 0 = 1\n",
    "$$\n",
    "\n",
    "and so \n",
    "\n",
    "$$\\mathbb{V}(Z) = \\mathbb{E}(Z^2) - \\mathbb{E}(Z)^2 = 1 - 0 = 1$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exponential**.  Let $X \\sim \\text{Exponential}(\\beta)$.  Then:\n",
    "\n",
    "- $ \\mathbb{E}(X) = \\int_0^\\infty x \\frac{1}{\\beta} e^{-x / \\beta} dx = \\frac{1}{\\beta} \\int_0^\\infty x e^{-x / \\beta} dx = \\frac{1}{\\beta} \\beta^2 = \\beta$\n",
    "- $\\mathbb{E}(X^2) =  \\int_0^\\infty x^2 \\frac{1}{\\beta} e^{-x / \\beta} dx = \\frac{1}{\\beta} \\int_0^\\infty x^2 e^{-x / \\beta} dx = \\frac{1}{\\beta} 2\\beta^3 = 2 \\beta^2 $\n",
    "- $ \\mathbb{V}(X) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2 = 2\\beta^2 - \\beta^2 = \\beta^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Gamma**.  Let $X \\sim \\text{Gamma}(\\alpha, \\beta)$.  The PDF is \n",
    "\n",
    "$$ f_X(x) = \\frac{\\beta^\\alpha}{\\Gamma(\\alpha)} x^{\\alpha - 1} e^{-\\beta x} \\quad \\text{for } x > 0 $$\n",
    "\n",
    "We have:\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\mathbb{E}(X) \n",
    "&= \\int x f_X(x) dx \\\\\n",
    "&= \\int_0^\\infty x \\frac{\\beta^\\alpha}{\\Gamma(\\alpha)} x^{\\alpha - 1} e^{-\\beta x} dx \\\\\n",
    "&= \\frac{\\alpha}{\\beta} \\int_0^\\infty\\frac{\\beta^{\\alpha + 1}}{\\Gamma(\\alpha + 1)} x^\\alpha e^{-\\beta x} dx \\\\\n",
    "&= \\frac{\\alpha}{\\beta}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where we used that\n",
    "\n",
    "- $\\alpha \\Gamma(\\alpha) = \\Gamma(\\alpha + 1)$,\n",
    "- and last integral is the PDF of $\\text{Gamma}(\\alpha + 1, \\beta)$, integrated over its entire domain.\n",
    "\n",
    "We also have:\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\mathbb{E}(X^2) \n",
    "&= \\int x^2 f_X(x) dx \\\\\n",
    "&= \\int_0^\\infty x^2 \\frac{\\beta^\\alpha}{\\Gamma(\\alpha)} x^{\\alpha - 1} e^{-\\beta x} dx \\\\\n",
    "&= \\frac{\\alpha (\\alpha + 1)}{\\beta^2} \\int_0^\\infty\\frac{\\beta^{\\alpha + 2}}{\\Gamma(\\alpha + 2)} x^{\\alpha + 1} e^{-\\beta x} dx \\\\\n",
    "&= \\frac{\\alpha (\\alpha + 1)}{\\beta^2}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "- $\\alpha (\\alpha + 1) \\Gamma(\\alpha + 1) = \\Gamma(\\alpha + 2)$,\n",
    "- and last integral is the PDF of $\\text{Gamma}(\\alpha + 2, \\beta)$, integrated over its entire domain.\n",
    "\n",
    "Therefore,\n",
    "\n",
    "$$ \\mathbb{V}(X) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2 = \\frac{\\alpha (\\alpha + 1)}{\\beta^2} - \\frac{\\alpha^2}{\\beta^2} = \\frac{\\alpha}{\\beta^2} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Beta**.  Let $X \\sim \\text{Beta}(\\alpha, \\beta)$.  The PDF is \n",
    "\n",
    "$$f_X(x) = \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha) \\Gamma(\\beta)} x^{\\alpha - 1}(1 - x)^{\\beta - 1} \\quad \\text{for } x > 0$$\n",
    "\n",
    "We have:\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\mathbb{E}(X) \n",
    "&= \\int x f_X(x) dx \\\\\n",
    "&= \\int_0^\\infty x \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha) \\Gamma(\\beta)} x^{\\alpha - 1}(1 - x)^{\\beta - 1} dx \\\\\n",
    "&= \\frac{\\alpha}{\\alpha + \\beta} \\int_0^\\infty \\frac{\\Gamma(\\alpha + \\beta + 1)}{\\Gamma(\\alpha + 1) \\Gamma(\\beta)} x^{\\alpha}(1 - x)^{\\beta - 1} dx \\\\\n",
    "&= \\frac{\\alpha}{\\alpha + \\beta}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where we used that\n",
    "\n",
    "- $\\alpha \\Gamma(\\alpha) = \\Gamma(\\alpha + 1)$,\n",
    "- $(\\alpha + \\beta) \\Gamma(\\alpha + \\beta) = \\Gamma(\\alpha + \\beta + 1)$,\n",
    "- and the last integral is the PDF of $\\text{Beta}(\\alpha + 1, \\beta)$, integrated over its entire domain.\n",
    "\n",
    "We also have:\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\mathbb{E}(X^2) \n",
    "&= \\int x^2 f_X(x) dx \\\\\n",
    "&= \\int_0^\\infty x^2 \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha) \\Gamma(\\beta)} x^{\\alpha - 1}(1 - x)^{\\beta - 1} dx \\\\\n",
    "&= \\frac{\\alpha (\\alpha + 1)}{(\\alpha + \\beta)(\\alpha + \\beta + 1)} \\int_0^\\infty \\frac{\\Gamma(\\alpha + \\beta + 2)}{\\Gamma(\\alpha + 2) \\Gamma(\\beta)} x^{\\alpha + 1}(1 - x)^{\\beta - 1} dx \\\\\n",
    "&= \\frac{\\alpha (\\alpha + 1)}{(\\alpha + \\beta)(\\alpha + \\beta + 1)}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where we used that\n",
    "\n",
    "- $\\alpha (\\alpha + 1) \\Gamma(\\alpha + 1) = \\Gamma(\\alpha + 2)$,\n",
    "- $(\\alpha + \\beta) (\\alpha + \\beta + 1) \\Gamma(\\alpha + \\beta + 1) = \\Gamma(\\alpha + \\beta + 2)$,\n",
    "- and the last integral is the PDF of $\\text{Beta}(\\alpha + 2, \\beta)$, integrated over its entire domain.\n",
    "\n",
    "Therefore,\n",
    "\n",
    "$$ \\mathbb{V}(X) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2 = \\frac{\\alpha (\\alpha + 1)}{(\\alpha + \\beta)(\\alpha + \\beta + 1)} - \\frac{\\alpha^2}{(\\alpha + \\beta)^2} = \\frac{\\alpha \\beta}{(\\alpha + \\beta)^2 (\\alpha + \\beta + 1)} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**t-student**.  Let $X \\sim t_\\nu$.  The PDF for the t-student distribution is\n",
    "\n",
    "$$ f_X(x) = \\frac{1}{\\sqrt{v \\pi}} \\frac{\\Gamma\\left(\\frac{\\nu + 1}{2}\\right)}{\\Gamma\\left(\\frac{\\nu}{2}\\right)} \\frac{1}{\\left(1 + \\frac{x^2}{\\nu} \\right)^{(\\nu + 1)/2}} $$\n",
    "\n",
    "Since the PDF is even, $f_X(x) = f_X(-x)$, the expectation will be 0 when it is defined:\n",
    "\n",
    "$$ \\mathbb{E}(X) = \\int_{-\\infty}^\\infty x f_X(x) dx = \\int_{-\\infty}^0 x f_X(x) dx + \\int_0^\\infty x f_X(x) dx = \n",
    "\\int_0^\\infty -x f_X(-x) dx + \\int_0^\\infty x f_X(x) dx = \\int_0^\\infty (-x + x)f_X(x) dx = 0 $$\n",
    "\n",
    "But \n",
    "\n",
    "$$ \\mathbb{E}(X) = \\int_{-\\infty}^\\infty x f_X(x) dx = \\frac{1}{\\sqrt{v \\pi}} \\frac{\\Gamma\\left(\\frac{\\nu + 1}{2}\\right)}{\\Gamma\\left(\\frac{\\nu}{2}\\right)} \\int_{-\\infty}^\\infty x  \\left(1 + \\frac{x^2}{\\nu} \\right)^{-(\\nu + 1)/2} dx $$\n",
    "\n",
    "For the expectation of $X^2$, assuming it is defined, we have:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\mathbb{E}(X^2) &= \\int_{-\\infty}^\\infty x^2 f_X(x) dx \\\\\n",
    "&= \\frac{1}{\\sqrt{v \\pi}} \\frac{\\Gamma\\left(\\frac{\\nu + 1}{2}\\right)}{\\Gamma\\left(\\frac{\\nu}{2}\\right)} \\int_{-\\infty}^\\infty x^2 \\left( 1 + \\frac{x^2}{\\nu}\\right)^{-(\\nu + 1) / 2} dx \\\\\n",
    "&= \\frac{\\nu}{\\sqrt{\\pi}} \\frac{\\Gamma\\left(\\frac{\\nu + 1}{2}\\right)}{\\Gamma\\left(\\frac{\\nu}{2}\\right)} \\int_0^1 y^{\\nu /2 - 2} \\left( 1 - y \\right)^{1 / 2} dy \\\\\n",
    "&= \\frac{\\nu}{\\sqrt{\\pi}} \\frac{\\Gamma\\left(\\frac{\\nu + 1}{2}\\right)}{\\Gamma\\left(\\frac{\\nu}{2}\\right)} \\frac{\\Gamma\\left(\\frac{\\nu}{2} - 1\\right) \\Gamma\\left(\\frac{3}{2}\\right)}{\\Gamma\\left(\\frac{\\nu + 1}{2}\\right)} \\\\\n",
    "&= \\frac{\\nu}{\\nu - 2}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where we used:\n",
    "\n",
    "- A variable replacement $y = \\left( 1 + \\frac{x^2}{\\nu} \\right)^{-1}$\n",
    "- The property that $\\int_0^1 y^{p - 1} (1 - y)^{q - 1} dy = \\frac{\\Gamma(p) \\Gamma(q)}{\\Gamma(p + q)}$, since this is the integral of the PDF of $\\Gamma(p, q)$ scaled by a factor of $\\frac{\\Gamma(p) \\Gamma(q)}{\\Gamma(p + q)}$, with $p = \\nu / 2 - 1$, $q = 3/2$\n",
    "- $\\Gamma(3 / 2) = \\sqrt{\\pi}$\n",
    "\n",
    "Finally,\n",
    "\n",
    "$$ \\mathbb{V}(X) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2 = \\frac{\\nu}{\\nu - 2} $$\n",
    "\n",
    "*Reference: https://math.stackexchange.com/a/1502519*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**$\\chi^2$ distribution**.  Let $X \\sim \\chi^2_k$.  Then $X$ has the same distributions as the sum of squares of $k$ IID standard Normal random variables, $X = \\sum_{i=1}^k Z_i^2$, $Z_i \\sim N(0, 1)$.\n",
    "\n",
    "The expectation of $X$ can then be computed:\n",
    "\n",
    "$$ \\mathbb{E}(X) = \\mathbb{E}\\left( \\sum_{i=1}^k Z_i^2 \\right) = \\sum_{i=1}^k \\mathbb{E}(Z_i^2) = \\sum_{i=1}^k (\\mathbb{V}(Z_i) + \\mathbb{E}(Z_i)^2) = \\sum_{i=1}^k (1 + 0) = k $$\n",
    "\n",
    "The expectation of $X^2$ is:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\mathbb{E}(X^2) &= \\mathbb{E}\\left( \\left( \\sum_{i=1}^k Z_i^2 \\right)^2 \\right) \\\\\n",
    "&= \\mathbb{E}\\left( \\sum_{i=1}^k Z_i^4 + \\sum_{i=1}^k \\sum_{j=1; j \\neq i}^k Z_i^2 Z_j^2 \\right) \\\\\n",
    "&= \\sum_{i=1}^k \\mathbb{E}(Z_i^4) + \\sum_{i=1}^k \\sum_{j=1; j \\neq i}^k \\mathbb{E}(Z_i^2) \\mathbb{E}(Z_j^2)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "But we have:\n",
    "\n",
    "$$ \\mathbb{E}(Z_i^2) = \\mathbb{V}(Z_i) + \\mathbb{E}(Z_i)^2 = 1 + 0 = 1 $$\n",
    "\n",
    "and, using moment generating functions,\n",
    "\n",
    "$$M_Z(t) = e^{t^2 / 2}$$\n",
    "\n",
    "and taking the fourth derivative,\n",
    "\n",
    "$$ M_Z^{(4)}(t) = 3 M_Z^{(2)}(t) + t M_Z^{(3)}(t)$$\n",
    "\n",
    "Setting $t = 0$ gives us $\\mathbb{E}(Z_i^4) = 3$.\n",
    "\n",
    "Replacing it back on the expectation expression for $X^2$,\n",
    "\n",
    "$$\n",
    "\\mathbb{E}(X^2) = \\sum_{i=1}^k 3 + \\sum_{i=1}^k \\sum_{j=1; j \\neq i}^k 1 \\cdot 1 = 3k + k(k-1) = k^2 + 2k\n",
    "$$\n",
    "\n",
    "Therefore,\n",
    "\n",
    "$$ \\mathbb{V}(X) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2 = k^2 + 2k - k^2 = 2k $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*The proofs for the multinomial and mutivariate normal distribution expressions are provided in the book text (and there are notes above).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.7.13**.  Suppose we generate a random variable $X$ in the following way.  First we flip a fair coin.  If the coin is heads, take $X$ to have a $\\text{Uniform}(0, 1)$ distribution.  If the coin is tails, take $X$ to have a $\\text{Uniform}(3, 4)$ distribution.\n",
    "\n",
    "**(a)** Find the mean of $X$.\n",
    "\n",
    "**(b)** Find the standard deviation of $X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  We have $X = C U_1 + (1 - C)U_2$, where $C \\sim \\text{Bernoulli}(1/2)$, $U_1 \\sim \\text{Uniform}(0, 1)$ and $U_2 \\sim \\text{Uniform}(3, 4)$ are all independent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(a)**\n",
    "\n",
    "$$\\mathbb{E}(X) = \\mathbb{E}(CU_1 + (1 - C)U_2) = \\mathbb{E}(C)\\mathbb{E}(U_1) + (1 - \\mathbb{E}(C))\\mathbb{E}(U_2) = \\frac{1}{2} \\left(\\frac{1}{2} + \\frac{7}{2}\\right) = 2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(b)**\n",
    "\n",
    "$$ X^2 = (CU_1 + (1 - C)U_2)^2 = C^2U_1^2 + (1 - C)^2 U_2^2 + 2C(1 - C)U_1U_2 = C^2U_1^2 + (1 - C)^2 U_2^2 $$\n",
    "\n",
    "so\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\mathbb{E}(X^2) &= \\mathbb{E}(C^2)\\mathbb{E}(U_1^2) + \\mathbb{E}((1 - C)^2) \\mathbb{E}(U_2^2) \\\\\n",
    "&= \\mathbb{E}(C) \\mathbb{E}(U_1^2) + \\mathbb{E}(1 - C) \\mathbb{E}(U_2^2) \\\\\n",
    "&= \\frac{1}{2} \\left( \\frac{1}{3} + \\frac{37}{3} \\right) = \\frac{19}{3}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "and then\n",
    "\n",
    "$$ \\mathbb{V}(X) = \\mathbb{E}(X^2) - \\mathbb{E}(X)^2 = \\frac{19}{3} - 2^2 = \\frac{7}{3} $$\n",
    "\n",
    "and so the standard deviation is $\\sqrt{\\mathbb{V}(X)} = \\sqrt{7/3}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.17.14**.  Let $X_1, \\dots, X_m$ and $Y_1, \\dots, Y_n$ be random variables and let $a_1, \\dots, a_m$ and $b_1, \\dots, b_n$ be constants.  Show that\n",
    "\n",
    "$$ \\text{Cov}\\left( \\sum_{i=1}^m a_i X_i , \\sum_{j=1}^n b_j Y_j \\right) = \\sum_{i=1}^m \\sum_{j=1}^n a_i b_j \\text{Cov}(X_i, Y_j) $$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  We have:\n",
    "\n",
    "$$ \n",
    "\\begin{align}\n",
    "\\text{Cov}\\left(\\sum_{i=1}^m a_i X_i, Y\\right) &= \\mathbb{E}\\left(\\left( \\sum_{i=1}^m a_i X_i \\right) Y\\right) - \\mathbb{E}\\left( \\sum_{i=1}^m a_i X_i \\right) \\mathbb{E}(Y) \\\\\n",
    "&= \\sum_{i=1}^m \\mathbb{E}(a_i X_i Y) - \\left( \\sum_{i=1}^m a_i \\mathbb{E}(X_i) \\right) \\mathbb{E}(Y) \\\\\n",
    "&= \\sum_{i=1}^m \\mathbb{E}(a_i X_i Y) -  a_i \\mathbb{E}(X_i) \\mathbb{E}(Y) \\\\\n",
    "&= \\sum_{i=1}^m a_i \\text{Cov}(X_i, Y)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "and, since $\\text{Cov}(A, B) = \\text{Cov}(B, A)$,\n",
    "\n",
    "$$ \\text{Cov}\\left(X, \\sum_{j=1}^n b_j Y_j \\right) = \\sum_{j=1}^n b_i \\text{Cov}(X, Y_j) $$\n",
    "\n",
    "Applying this for each $X_i$, we get the result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.17.15**.  Let\n",
    "\n",
    "$$ f_{X, Y} = \\begin{cases}\n",
    "\\frac{1}{3} (x + y) &\\text{if } 0 \\leq x \\leq 1, 0 \\leq y \\leq 2 \\\\\n",
    "0 &\\text{otherwise}\n",
    "\\end{cases}$$\n",
    "\n",
    "Find $\\mathbb{V}(2X - 3Y + 8)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  Let $r(x, y) = 2x - 3y$.  Then:\n",
    "\n",
    "$$ \\mathbb{V}(2X - 3Y + 8) = \\mathbb{V}(2X - 3Y) = \\mathbb{V}(r(X, Y)) $$\n",
    "\n",
    "Calculating the expectation of $r(X, Y)$ and $r(X, Y)^2$:\n",
    "\n",
    "$$ \\mathbb{E}(r(X, Y)) = \\int_0^1 \\int_0^2 r(x, y) f(x, y) dy dx = \\int_0^1 \\int_0^2 \\frac{1}{3}(2x - 3y)(x + y) dy dx \n",
    "= \\int_0^1 \\frac{2}{3}(2x^2 - x - 4) dx = -\\frac{23}{9} $$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\mathbb{E}(r(X, Y)^2) = \\int_0^1 \\int_0^2 r(x, y)^2 f(x, y) dy dx = \\int_0^1 \\int_0^2 \\frac{1}{3}(2x - 3y)^2(x + y) dy dx \n",
    "= \\int_0^1 \\frac{4}{3}(2x^3 - 4x^2 - 2x + 9) dx = \\frac{86}{9} $$\n",
    "\n",
    "and so\n",
    "\n",
    "$$ \\mathbb{V}(r(X, Y)) = \\mathbb{E}(r(X, Y)^2) - \\mathbb{E}(r(X, Y))^2 = \\frac{86}{9} - \\frac{23^2}{9^2} = \\frac{245}{81} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.17.16**.  Let $r(x)$ be a function of $x$ and let $s(y)$ be a function of $y$.  Show that\n",
    "\n",
    "$$ \\mathbb{E}(r(X) s(Y) | X) = r(X) \\mathbb{E}(s(Y) | X) $$\n",
    "\n",
    "Also, show that $\\mathbb{E}(r(X) | X) = r(X)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  We have:\n",
    "\n",
    "$$ \\mathbb{E}(r(X) s(Y) | X = x) = \\int r(x) s(y) f(x, y) dy = r(x) \\int s(y) f(x, y) dy = r(x) \\mathbb{E}(s(Y) | X = x) $$\n",
    "\n",
    "and so the random variable $\\mathbb{E}(r(X) s(Y) | X)$ takes the same value as the variable $r(X) \\mathbb{E}(s(Y) | X)$ for each $X = x$ -- therefore the random variables are equal.\n",
    "\n",
    "In particular, when $s(y) = 1$ for all $y$, we have $\\mathbb{E}(r(X) | X) = r(X)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.17.17**.  Prove that\n",
    "\n",
    "$$ \\mathbb{V}(Y) = \\mathbb{E} \\mathbb{V} (Y | X) + \\mathbb{V} \\mathbb{E} (Y | X) $$\n",
    "\n",
    "Hint:  Let $m = \\mathbb{E}(Y)$ and let $b(x) = \\mathbb{E}(Y | X = x)$.  Note that $\\mathbb{E}(b(X)) = \\mathbb{E} \\mathbb{E}(Y | X) = \\mathbb{E}(Y) = m$.  Bear in mind that $b$ is a function of $x$.  Now write \n",
    "\n",
    "$$\\mathbb{V}(Y) = \\mathbb{E}((Y - m)^2) = \\mathbb{E}(((Y - b(X)) + (b(X) - m))^2)$$\n",
    "\n",
    "Expand the square and take the expectation.  You then have to take the expectation of three terms.  In each case, use the rule of iterated expectation, i.e. $\\mathbb{E}(\\text{stuff}) = \\mathbb{E}(\\mathbb{E}(\\text{stuff} | X))$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  We have:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\mathbb{V}(Y) &= \\mathbb{E}(Y^2) - \\mathbb{E}(Y)^2 \\\\\n",
    "&= \\mathbb{E}(\\mathbb{E}(Y^2 | X)) - \\mathbb{E}(\\mathbb{E}(Y | X))^2 \\\\\n",
    "&= \\mathbb{E}\\left( \\mathbb{V}(Y | X) + \\mathbb{E}(Y | X)^2 \\right) - \\mathbb{E}(\\mathbb{E}(Y | X))^2 \\\\\n",
    "&= \\mathbb{E}(\\mathbb{V}(Y | X)) + \\left( \\mathbb{E}(\\mathbb{E}(Y | X)^2) - \\mathbb{E}(\\mathbb{E}(Y | X))^2 \\right) \\\\\n",
    "&= \\mathbb{E} (\\mathbb{V}(Y | X) + \\mathbb{V}(\\mathbb{E}(Y | X))\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.17.18**.  Show that if $\\mathbb{E}(X | Y = y) = c $ for some constant $c$ then $X$ and $Y$ are uncorrelated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.  We have:\n",
    "\n",
    "$$ \\mathbb{E}(XY) = \\int \\mathbb{E}(XY | Y = y) dF_Y(y) = \\int y \\mathbb{E}(X | Y = y) dF_Y(y) = \\int cy \\mathbb{E}(X | Y = y) dF_Y(y) = c \\; \\mathbb{E}(Y)$$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\mathbb{E}(X) = \\mathbb{E}(\\mathbb{E}(X | Y)) = \\mathbb{E}(c) = c $$\n",
    "\n",
    "so $\\mathbb{E}(XY) = \\mathbb{E}(X) \\mathbb{E}(Y)$, and so $\\text{Cov}(X, Y) = 0$, and so $X$ and $Y$ are uncorrelated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.17.19**.  This question is to help you understand the idea of **sampling distribution**.  Let $X_1, \\dots, X_n$ be IID with mean $\\mu$ and variance $\\sigma^2$.  Let $\\overline{X}_n  = n^{-1}\\sum_{i=1}^n X_i$.  Then $\\overline{X}_n$ is a **statistic**, that is, a function of the data.  Since $\\overline{X}_n$ is a random variable, it has a distribution.  This distribution is called the *sampling distribution of the statistic*.  Recall from Theorem 4.16 that $\\mathbb{E}(\\overline{X}_n) = \\mu$ and $\\mathbb{V}(\\overline{X}_n) = \\sigma^2 / n$.  Don't confuse the distribution of the data $f_X$ and the distribution of the statistic $f_{\\overline{X}_n}$.  To make this clear, let $X_1, \\dots, X_n \\sim \\text{Uniform}(0, 1)$.  Let $f_X$ be the density of the $\\text{Uniform}(0, 1)$.  Plot $f_X$.  Now let $\\overline{X}_n = n^{-1} \\sum_{i=1}^n X_i$.  Find $\\mathbb{E}(\\overline{X}_n)$ and $\\mathbb{V}(\\overline{X}_n)$.  Plot them as a function of $n$.  Comment.  Now simulate the distribution of $\\overline{X}_n$ for $n = 1, 5, 25, 100$.  Check the simulated values of $\\mathbb{E}(\\overline{X}_n)$ and $\\mathbb{V}(\\overline{X}_n)$ agree with your theoretical calculations.  What do you notice about the sampling distribution of $\\overline{X}_n$ as it increases?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.\n",
    "\n",
    "$$ \\mathbb{E}\\left(\\overline{X}_n\\right) = \\mathbb{E}\\left(n^{-1} \\sum_{i=1}^n X_i \\right) = n^{-1} \\sum_{i=1}^n \\mathbb{E}(X_i) = \\frac{1}{2} $$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\mathbb{V}\\left(\\overline{X}_n\\right) = \\mathbb{V}\\left(n^{-1} \\sum_{i=1}^n X_i \\right) = n^{-2} \\sum_{i=1}^n \\mathbb{V}(X_i) = \\frac{1}{12 n} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.random.seed(0)\n",
    "\n",
    "B = 1000\n",
    "\n",
    "E_overline_X = np.empty(100)\n",
    "V_overline_X = np.empty(100)\n",
    "\n",
    "for n in range(1, 101):\n",
    "    X_n = np.random.uniform(low=0, high=1, size=(B, n)).mean(axis=1)\n",
    "    E_overline_X[n - 1] = X_n.mean()\n",
    "    V_overline_X[n - 1] = X_n.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "\n",
    "ax = plt.subplot(212)\n",
    "ax.hlines(0, xmin=-0.5, xmax=0, color='C0')\n",
    "ax.hlines(1, xmin=0, xmax=1, color='C0')\n",
    "ax.hlines(0, xmin=1, xmax=1.5, color='C0')\n",
    "ax.vlines([0, 1], ymin=0, ymax=1, color='C0', linestyle='dashed')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel(r'$f_X(x)$')\n",
    "ax.set_title('Density of Uniform(0, 1)')\n",
    "\n",
    "nn = np.arange(1, 101)\n",
    "\n",
    "ax = plt.subplot(221)\n",
    "ax.plot(nn, 1/2 * np.ones(100), label='Calculated')\n",
    "ax.plot(nn, E_overline_X, label='Measured')\n",
    "ax.set_xlabel('n')\n",
    "ax.set_ylabel(r'$\\mathbb{E}(\\overline{X}_n)$')\n",
    "ax.set_title('Sampling distribution mean')\n",
    "ax.legend(loc='lower right')\n",
    "\n",
    "ax = plt.subplot(222)\n",
    "ax.plot(nn, 1 / (12 * nn), label='Calculated')\n",
    "ax.plot(nn, V_overline_X, label='Measured')\n",
    "ax.set_xlabel('n')\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylabel(r'$\\mathbb{V}(\\overline{X}_n)$')\n",
    "ax.set_title('Sampling distribution variance')\n",
    "ax.legend(loc='upper right')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculated and simulated values agree."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.17.20**.  Prove Lemma 4.20.\n",
    "\n",
    "If $a$ is a vector and $X$ is a random vector with mean $\\mu$ and variance $\\Sigma$ then\n",
    "\n",
    "$$ \\mathbb{E}(a^T X) = a^T \\mu\n",
    "\\quad \\text{and} \\quad\n",
    "\\mathbb{V}(a^T X) = a^T \\Sigma a $$\n",
    "\n",
    "If $A$ is a matrix then\n",
    "\n",
    "$$ \\mathbb{E}(A X) = A \\mu\n",
    "\\quad \\text{and} \\quad\n",
    "\\mathbb{V}(AX) = A \\Sigma A^T $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**.\n",
    "\n",
    "We have:\n",
    "\n",
    "$$ \\mathbb{E}(a^T X) = \\begin{pmatrix}\n",
    "\\mathbb{E}(a_1 X_1) \\\\\n",
    "\\mathbb{E}(a_2 X_2) \\\\\n",
    "\\cdots \\\\\n",
    "\\mathbb{E}(a_k X_k)\n",
    "\\end{pmatrix} = \\begin{pmatrix}\n",
    "a_1 \\mathbb{E}(X_1) \\\\\n",
    "\\mathbb{E}(X_2) \\\\\n",
    "\\cdots \\\\\n",
    "\\mathbb{E}(X_k)\n",
    "\\end{pmatrix} = a^T \\mu $$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\mathbb{V}(a^T X) = \\mathbb{E}((a^T (X - \\mu) (a^T(X - \\mu))^T) = \\mathbb{E}((a^T (X - \\mu) (X - \\mu)^T a) = a^T \\Sigma a $$\n",
    "\n",
    "Similarly, for the matrix case,\n",
    "\n",
    "$$ \\mathbb{E}(AX) = \\begin{pmatrix}\n",
    "\\mathbb{E}\\left( \\sum_{j=1}^k a_{1, j} X_j \\right) \\\\\n",
    "\\mathbb{E}\\left( \\sum_{j=1}^k a_{2, j} X_j \\right) \\\\\n",
    "\\cdots \\\\\n",
    "\\mathbb{E}\\left( \\sum_{j=1}^k a_{k, j} X_j \\right) \\\\\n",
    "\\end{pmatrix} = \\begin{pmatrix}\n",
    "\\sum_{j=1}^k a_{1, j} \\mathbb{E}(X_j) \\\\\n",
    "\\sum_{j=1}^k a_{2, j} \\mathbb{E}(X_j) \\\\\n",
    "\\cdots \\\\\n",
    "\\sum_{j=1}^k a_{k, j} \\mathbb{E}(X_j) \\\\\n",
    "\\end{pmatrix} = A \\mu $$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\mathbb{V}(A X) = \\mathbb{E}((A (X - \\mu) (A(X - \\mu))^T) = \\mathbb{E}((A (X - \\mu) (X - \\mu)^T A^T) = A \\Sigma A^T $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4.17.21**. Let $X$ and $Y$ be random variables. Suppose that $\\mathbb{E}(Y|X) = X$. Show that Cov$(Y, X) = \\mathbb{V}(X)$.\n",
    "\n",
    "**Solution**.\n",
    "We know that\n",
    "$$Cov(X, Y)$$\n",
    "$$= \\mathbb{E}(X \\cdot Y) - \\mathbb{E}(X) \\cdot \\mathbb{E}(Y)$$\n",
    "$$= \\mathbb{E}(X \\cdot Y) - \\mathbb{E}(X) \\cdot \\mathbb{E}(\\mathbb{E}(Y|X))$$\n",
    "$$= \\mathbb{E}(X\\cdot Y) - \\mathbb{E}(X) \\cdot \\mathbb{E}(X)$$\n",
    "\n",
    "Hence we only need to show that \n",
    "$$\\mathbb{E}(X\\cdot Y) = \\mathbb{E}(X \\cdot \\mathbb{E}(Y|X))$$\n",
    "\n",
    "This is true, since $E(Y) = EE(Y|X)$. Therefore\n",
    "$$Cov(X, Y)$$\n",
    "$$= \\mathbb{E}(X\\cdot Y) -  \\mathbb{E}(X) \\cdot \\mathbb{E}(X)$$\n",
    "$$= \\mathbb{E}(X \\cdot \\mathbb{E}(Y|X)) -  \\mathbb{E}(X) \\cdot \\mathbb{E}(X)$$\n",
    "$$= \\mathbb{E}(X\\cdot X) -  \\mathbb{E}(X) \\cdot \\mathbb{E}(X)$$\n",
    "$$= Cov(X, X)$$\n",
    "$$= V(X)$$"
   ]
  }
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