diff --git a/A1.ipynb b/A1.ipynb new file mode 100644 index 0000000..6dd71ce --- /dev/null +++ b/A1.ipynb @@ -0,0 +1,507 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "55b6fde2-ab8d-4941-9bd5-ea01d17be87c", + "metadata": {}, + "source": [ + "**1(a)**" + ] + }, + { + "cell_type": "markdown", + "id": "6ad61f9a-3b9a-476a-83f1-635aefc34ccc", + "metadata": {}, + "source": [ + "Here is the image content converted to LaTeX format:\n", + "\n", + "\\begin{align*}\n", + "&\\text{Let $X$ be a random variable with the parameters $n$, $p$. Then under the following} \\\\\n", + "&\\text{conditions $X$ tends to Poisson distribution:} \\\\\n", + "&\\quad 1) \\quad n,p^{-1} \\to \\infty \\\\\n", + "&\\quad 2) \\quad \\lambda = np \\to \\text{constant} \\\\\n", + "&\\text{Now, } \\quad b(x; n, p) = \\quad \\binom{n}{x} p^x q^{n-x} \\quad \\therefore \\quad p = \\frac{\\lambda}{n} \\quad \\& \\quad q = 1 - \\frac{\\lambda}{n}\\\\\n", + "&\\text{Then, } \\quad b(x; n, p) = \\binom{n}{x} \\left(\\frac{\\lambda}{n}\\right)^{x} \\left(1 - \\frac{\\lambda}{n}\\right)^{n-x}\\\\\n", + "&\\quad = \\frac{n(n-1) \\cdots (n-x+1)}{x!} \\quad \\frac{\\lambda^x}{n^x} \\left(1 - \\frac{\\lambda}{n}\\right)^{n-x} \\\\\n", + "&\\quad = 1 \\cdot \\left(1 - \\frac{\\lambda_n}{n}\\right) \\left(1 - \\frac{2}{n}\\right) \\cdots \\left(1 - \\frac{x-1}{n}\\right) \\lambda^x \\frac{(1 - \\frac{\\lambda}{n})^n}{(1 - \\frac{\\lambda}{n})^x} \\frac{1}{x!} \\\\\n", + "&\\therefore \\quad \\lim_{n \\to \\infty} b(x; n, p) = \\quad \\frac{\\lambda^x}{x!} \\cdot e^{-\\lambda} = e^{-\\lambda} \\lambda^x \\quad \\therefore \\quad X \\to p(\\lambda)\n", + "\\end{align*}" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "dc10fd41-f113-4384-855c-924e29d73195", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.stats import binom, poisson\n", + "import seaborn as sns" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "7f7c4af7-8119-4cda-892b-16805f5c02ec", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def rms_error(y_pred, y_true):\n", + " return np.sqrt(np.mean((y_pred - y_true) ** 2))" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "id": "97a4169b-3e3e-491d-8315-287e1d98e79d", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "n = 1000\n", + "p = 0.01\n", + "lam = 10\n", + "\n", + "x_values = np.arange(0, 30)\n", + "binomial_probs = np.array([binom.pmf(x, n, p) for x in x_values])\n", + "poisson_probs = np.array([poisson.pmf(x, lam) for x in x_values])" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "ce255e51-3986-4e1f-87fc-411a6cd84ccd", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.bar(x_values, binomial_probs, label='Binomial (n={}, p={})'.format(n, p), alpha=0.5)\n", + "plt.bar(x_values, poisson_probs, label='Poisson (lambda={})'.format(lam), alpha=0.5)\n", + "plt.title('Comparison of Poisson and Binomial Distributions')\n", + "plt.xlabel('x')\n", + "plt.ylabel('Probability')\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "d8c5cd6f-65bb-4f5d-96f0-7d9d775e60ba", + "metadata": {}, + "source": [ + "**1(b)**" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "143daeb5-5f69-41a7-8603-03c693cded03", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def plot_n_err(n,p):\n", + " lam = n*p\n", + " x_values = np.arange(0, 20)\n", + " y_tru = np.array([binom.pmf(x, n, p) for x in x_values])\n", + " y_pred= np.array([poisson.pmf(x, lam) for x in x_values])\n", + " plt.figure(figsize=(10, 6))\n", + " plt.bar(x_values, y_tru, label='Binomial (n={}, p={})'.format(n, p), alpha=0.5)\n", + " plt.bar(x_values, y_pred, label='Poisson (lambda={})'.format(lam), alpha=0.5)\n", + " plt.title('Comparison of Poisson and Binomial Distributions')\n", + " plt.xlabel('x')\n", + " plt.ylabel('Probability')\n", + " plt.legend()\n", + " plt.grid(True)\n", + " plt.show()\n", + "\n", + " rmse = rms_error(y_pred, y_tru)\n", + " print(lam)\n", + " print(\"Root Mean Square Error:\", rmse)" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "id": "13db97bd-aad7-42e2-a8ee-9c895786a9c8", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4.6000000000000005\n", + "Root Mean Square Error: 0.009746956007480781\n" + ] + } + ], + "source": [ + "plot_n_err(20,0.23)" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "dcdb7ceb-e59f-491f-9d93-7c5eb4862514", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.3\n", + "Root Mean Square Error: 5.053026257673285e-08\n" + ] + } + ], + "source": [ + "plot_n_err(3*1e5,1e-6)" + ] + }, + { + "cell_type": "markdown", + "id": "52d2c13b-1858-4a8e-9219-a3b795943b6f", + "metadata": {}, + "source": [ + "From the above two graphs we can infer that if $\\lambda = 4 $ there is a relatively high error but when $\\lambda = 0.3 << 5$ we get a pretty accurate approximation" + ] + }, + { + "cell_type": "markdown", + "id": "4512fd88-154f-4a81-a695-e2e5b93e9c2a", + "metadata": {}, + "source": [ + "**Q2**\n", + "\\begin{align*}\n", + "W &= X+XY+Y \\\\\n", + "Z &= XY^2+X^3Y \\\\\n", + "E[X] &= E\\left[E(X|Y)\\right] = E\\left[XE(Y|X)\\right] = E\\left[X\\cdot sX\\right] \\\\\n", + "\\text{As} \\quad Y&|X \\sim N(sX, 1-s^2) \\\\\n", + "\\therefore E[XY] &= sE[X^2] = s \\\\\n", + "E[X^2Y] &= E[X^2E(Y|X)] = E[sX^3] = s\\cdot 0 = 0 \\\\\n", + "E[XY^2] &= E\\left[E(XY^2|Y)\\right] = E\\left[Y^2E(X|Y)\\right] = sE(Y^3) = 0 \\\\\n", + "\\therefore E[X^3Y] &= E\\left[E(X^3Y|X)\\right] = E\\left[X^3E(Y|X)\\right] = sE(X^4)= 3s \\\\\n", + "E(w)E(Z) &= (s+0+0)(3s+3s) = 6s^2 \\\\\n", + "WZ &= (XY+XY+XY^2)(XY^2+X^3Y) \\\\\n", + "&= X^2Y^4+X^4Y^2+X^3Y^4+X^3Y^3+X^3Y^2+X^4Y^3 \\\\\n", + "E[X^2Y^4] &= E\\left[Y^4E[X^2|Y]\\right] \\\\\n", + "X|Y &\\sim N(sY,1-s^2) \\\\\n", + "E[X^2|Y] &= Var(X|Y) + \\left(E[X|Y]\\right)^2 \\\\\n", + "&= (1-s^2+s^2Y^2) = 1+s^2(Y^2-1) \\\\\n", + "\\therefore E[X^2Y^4] &= E\\left[Y^4+s^2Y^4-Y^6 s^2\\right] \\\\\n", + "&= E[Y^4]+s^2E[Y^4]-s^2E[Y^6] \\\\\n", + "&= 3+s^2(3)-s^2 15 \\\\\n", + "&= 3-12s^2 \\\\\n", + "E[X^4Y^2] &= 3-12s^2 \\\\\n", + "\\therefore E[WZ] &= 2(3-12s^2) = 6-24s^2 \\\\\n", + "Cov(W,Z) &= 6-24s^2-6s^2 = 6-30s^2\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "id": "1395260d-bef0-487d-9257-71b777adafca", + "metadata": {}, + "source": [ + "**Q3**\n", + "\\begin{align*}\n", + "&\\text{We know that} \\quad E(X_n) = \\mu \\quad \\text{and} \\quad \\text{Var}(X_n) = \\frac{\\sigma^{2}}{n} \\quad \\text{Then, by Chebyshev's inequality}\\\\\n", + "&P(|X_n - \\mu| \\le \\epsilon) = P\\left(\\left|X_n - \\mu\\right| < \\frac{\\epsilon}{\\frac{\\sigma}{\\sqrt{n}}} \\cdot \\frac{\\sigma}{\\sqrt{n}} \\right) \\ge \\left(1 - \\frac{1}{{\\left(\\frac{\\epsilon}{\\frac{\\sigma}{\\sqrt{n}}}\\right)}^{2}}\\right)\\\\\n", + "&\\text{Choose } n > \\frac{\\sigma^2}{\\epsilon^2 \\delta} \\quad (\\text{by WLLN})\\\\\n", + "&\\implies \\delta \\ge \\frac{\\sigma^2}{n \\epsilon^2}\\\\\n", + "&\\therefore P(|X_n - \\mu| \\le \\epsilon) \\ge 1 - \\frac{\\sigma^2}{n \\epsilon^2}\\\\\n", + "&\\therefore \\lim_{n \\to \\infty} P(|X_n - \\mu| < \\epsilon) \\to 1\\\\\n", + "&\\implies \\lim_{n \\to \\infty} P(|X_n - \\mu| \\ge \\epsilon) \\to 0\n", + "\\end{align*}\n" + ] + }, + { + "cell_type": "markdown", + "id": "a3c9afd9-5fa3-434c-b5f5-e6e63724d38f", + "metadata": {}, + "source": [ + "**Q4**\n", + "\n", + "My enrollment number is: $23112009$. Hence, the distribution will be as follows\n", + "\\\n", + "\\begin{array}{|c|c|c|c|c|c|c|c|c|}\n", + "\\hline\n", + "X & 0 & 1 & 2 & 3 & 9\\\\\n", + "\\hline\n", + "P(X=x) & \\frac{0}{18} & \\frac{2}{18} & \\frac{4}{18} & \\frac{3}{18} & \\frac{9}{18} \\\\\n", + "\\hline\n", + "\\end{array}\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "3e95d6c4-dfe4-4cb6-b7c5-4f544dc18828", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5.549\n" + ] + } + ], + "source": [ + "X = [0,1,2,3,9]\n", + "p = [0,0.11,0.22,0.17,0.5]\n", + "samples = np.random.choice(X, size=10000, p=p)\n", + "avg = sum(samples)/10000\n", + "print(avg)" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "f6851279-bad7-4da1-9fd3-1cc6577dd894", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "num_samples = 10000\n", + "num_repetitions = 10000\n", + "\n", + "# List to store the means\n", + "mean_values = []\n", + "\n", + "# Repeat the sampling process\n", + "for _ in range(num_repetitions):\n", + " # Sample from the array with the given probabilities\n", + " samples = np.random.choice(X, size=num_samples, p=p)\n", + " # Calculate the mean of the samples and append to the list\n", + " mean_values.append(np.mean(samples))\n", + "\n", + "sns.histplot(mean_values, kde=True)\n", + "plt.title('Frequency Histogram of Means')\n", + "plt.xlabel('Mean')\n", + "plt.ylabel('Frequency')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "b7c78792-8ce6-4809-a394-f59feccf2176", + "metadata": {}, + "source": [ + "The resultant graph follows Normal distribution as a courtesy of CLT" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "id": "48b0c7d6-2827-4285-ab09-c696df17b32d", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "mu = np.mean(mean_values)\n", + "sig = np.std(mean_values)" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "id": "f414ec5a-5685-4aba-a799-964fbe71bad9", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mean is -1.4574652595911176e-14\n", + "standard deviation is 1.0\n" + ] + } + ], + "source": [ + "Y = [(mean_values[i]-mu)/sig for i in range(10000)]\n", + "print('mean is ',np.mean(Y))\n", + "print('standard deviation is', np.std(Y))" + ] + }, + { + "cell_type": "markdown", + "id": "56a3ca18-a523-435e-a43c-3f3b7410797e", + "metadata": {}, + "source": [ + "Hence, CLT is verified as \\begin{equation*}\n", + "Y \\to N(0,1)\n", + "\\end{equation*}\n" + ] + }, + { + "cell_type": "markdown", + "id": "eb555d53-9236-4fb3-a813-5292a1f9ce9f", + "metadata": {}, + "source": [ + "**Q5)**\n", + "\\begin{equation*}\n", + "f(x,y) = \\begin{cases}\n", + "1, & 0 \\leq x < \\infty, \\quad 0 \\leq y \\leq e^{-x} \\\\\n", + "0, & \\text{otherwise}\n", + "\\end{cases}\n", + "\\end{equation*}\n", + "\n", + "\\begin{align*}\n", + "f_X(x) &= \\int_{0}^{e^{-x}} f_{X,Y}(x,y) \\, dy = \\int_{0}^{e^{-x}} 1 \\, dy = e^{-x} \\\\\n", + "f_Y(y) &= \\int_{0}^{-\\ln y} 1 \\, dx = -\\ln y \\quad \\text{if } y \\leq e^{-x} \\\\\n", + "\\therefore \\, f_{X,Y}(x,y) &\\neq f_X(x) \\cdot f_Y(y)\n", + "\\end{align*}\n", + "\n", + "Conditional probability cannot be calculated. Instead we can calculate $f(y|x)$:\n", + "\n", + "\\begin{align*}\n", + "f(y|x) &= \\frac{f_{X,Y}(x,y)}{f_X(x)} dx = \\int_{0}^{-\\ln y} \\frac{1}{e^{-x}} dx = e^{-\\ln y} - e^{0} = \\frac{1 - y}{y}\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "id": "816fdba8-fd90-4f1a-932c-65660a940aa8", + "metadata": {}, + "source": [ + "**Q7**\n", + "\\begin{align*}\n", + "f(x,y) = \\frac{1}{2\\pi\\sqrt{1-s^2}}e^{\\left(-\\frac{(x^2-2sxy+y^2)}{2(1-s^2)}\\right)}\n", + "\\end{align*}\n", + "\n", + "\\begin{align*}\n", + "f(x,y) &= c\\exp\\left(2\\pi^2y^2(1-s^2)\\right)\\int_{-\\infty}^{\\infty}\\exp(-t^2)\\cdot\\frac{dt}{\\sqrt{2\\pi c}} \\\\\n", + "&= c\\exp(-2\\pi^2y^2(1-s^2))\\cdot\\sqrt{\\frac{\\pi}{2\\pi c}} \\\\\n", + "&= \\frac{1}{\\sqrt{2\\pi}}\\exp\\left(-2\\pi^2\\cdot\\frac{1}{4\\pi^2(1-s^2)}y^2(1-s^2)\\right) \\\\\n", + "&= \\frac{1}{\\sqrt{2\\pi}}\\exp\\left(-\\frac{y^2}{2}\\right) \\quad\\Rightarrow\\quad Y\\sim N(0,1)\n", + "\\end{align*}\n", + "Similarly, $X\\sim N(0,1)$ as it is symmetric in $x$ and $y$.\n", + "\n", + "Set $X=Z_1$ and $Y=Z_2\\sqrt{1-s^2}+sZ_1$,\n", + "\\begin{align*}\n", + "aX+bY &= (a+bs)Z_1 + b\\sqrt{1-s^2}Z_2.\n", + "\\end{align*}\n", + "Now, $Var(X)=Var(Y)=1$\n", + "\n", + "\\begin{align*}\n", + "Cov(X,Y) &= Cov\\left(Z_1,sZ_1+\\sqrt{1-s^2}Z_2\\right) \\\\\n", + "&= s Cov(Z_1,Z_1) + \\sqrt{1-s^2}Cov(Z_1,Z_2) \\\\\n", + "&= s\\cdot 1 + \\sqrt{1-s^2}\\cdot 0 \\\\\n", + "&= s\n", + "\\end{align*}\n", + "\\begin{align*}\n", + "Corr(X^2,Y^2) &= \\frac{Cov(X^2,Y^2)}{\\sqrt{Var(X^2)Var(Y^2)}} \\\\\n", + "Cov(X^2,Y^2) &= E[X^2Y^2] - E[X^2]E[Y^2] \\\\\n", + "E[X^2Y^2] &= E\\left[E(X^2Y^2|X)\\right] = E\\left[X^2E(Y^2|X)\\right] \\\\\n", + "E(Y^2|X) &= Var(Y|X)+[E(Y|X)]^2\n", + "\\end{align*}\n", + "And, $Y|X\\sim N(sX,1-s^2)$\n", + "\\begin{align*}\n", + "E[Y^2|X] &= (1-s^2)+s^2X^2 = 1+s^2(X^2-1) \\\\\n", + "E[X^2Y^2] &= E\\left[X^2(1+s^2(X^2-1))\\right]\n", + "\\end{align*}\n", + "\n", + "\\begin{align*}\n", + "&= E\\left[X^2-s^2X^2+s^2X^4\\right] \\\\\n", + "&= (1-s^2)E[X^2]+s^2E[X^4] \\\\\n", + "&= (1-s^2)\\cdot 1 + s^2(3) \\\\\n", + "&= 1+2s^2 \\\\\n", + "Cov(X^2,Y^2) &= (1+2s^2)-1 = +2s^2 \\\\\n", + "Corr(X^2,Y^2) &= \\frac{2s^2}{\\sqrt{2\\cdot 2}} = s^2\n", + "\\end{align*}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d981982a-b77b-40e5-b6e1-273f22dcca64", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/README.md b/README.md index bead1d9..e9daca7 100644 --- a/README.md +++ b/README.md @@ -1,29 +1,8 @@ -# dsg-lecture-assignments -This is the official repository to submit dsg open assignments. -### Assignment Submission Guidelines -1. submission format - - EnrollmentNumber_Name / - - assignment_1 / - - [Files for assignment 1] - - assignment_2 / - - [Files for assignment 2] - - assignment_3 / - - [Files for assignment 3] - -2. Completion of All Assignments: - - We will only review the assignments of students who have completed all previous tasks. This ensures a comprehensive understanding of the topics and a more fruitful review process. - -3. Assignment Review: - - Once you have submitted all the required assignments, we will review your work. - -### How to Submit: - - fork this repo, complete the assignment, make a pull request in this repo. - -NOTE : we would monitor your progress continuously through git commits so if you just add all assignments at once then we won't consider your work. So keep adding your work incrementally. - -We encourage you to engage deeply with the assignments and reach out if you have any questions or need clarification on any topic. - -Best regards, - -Data Science Group +- **23112009 Rajdeep Aher** + - **assignment_1** + - A1.ipynb + - **assignment_2** + - [Files for assignment 2] + - **assignment_3** + - [Files for assignment 3]