Merge pull request #291 from pieteradejong/master

[MRG] ch1: add desc Expected Value; ch2: adds titles to some plots

Author: CamDavidsonPilon

Chapter1_Introduction/Chapter1.ipynb

@@ -394,6 +394,9 @@
     "\n",
     "- **$Z$ is mixed**: Mixed random variables assign probabilities to both discrete and continuous random variables, i.e. it is a combination of the above two categories. \n",
     "\n",
+    "#### Expected Value\n",
+    "Expected value (EV) is one of the most important concepts in probability. The EV for a given probability distribution can be described as \"the mean value in the long run for many repeated samples from that distribution.\" To borrow a metaphor from physics, a distribution's EV as like its \"center of mass.\" Imagine repeating the same experiment many times over, and taking the average over each outcome. The more you repeat the experiment, the closer this average will become to the distributions EV. (side note: as the number of repeated experiments goes to infinity, the difference between the average outcome and the EV becomes arbitrarily small.)\n",
+    "\n",
     "### Discrete Case\n",
     "If $Z$ is discrete, then its distribution is called a *probability mass function*, which measures the probability $Z$ takes on the value $k$, denoted $P(Z=k)$. Note that the probability mass function completely describes the random variable $Z$, that is, if we know the mass function, we know how $Z$ should behave. There are popular probability mass functions that consistently appear: we will introduce them as needed, but let's introduce the first very useful probability mass function. We say $Z$ is *Poisson*-distributed if:\n",
     "\n",

Chapter2_MorePyMC/Chapter2.ipynb

@@ -639,7 +639,7 @@
     "    plt.xlim(0, 80)\n",
     "\n",
     "figsize(12.5, 5)\n",
-    "plt.title(\"More example of artificial datasets\")\n",
+    "plt.suptitle(\"More examples of artificial datasets\", fontsize=14)\n",
     "for i in range(1, 5):\n",
     "    plt.subplot(4, 1, i)\n",
     "    plot_artificial_sms_dataset()"
@@ -1672,6 +1672,7 @@
     "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\")\n",
     "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\")\n",
     "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\")\n",
+    "plt.title(\"Logistic functon plotted for several value of $\\\\beta$ parameter\", fontsize=14)\n",
     "plt.legend();"
    ]
   },
@@ -1721,6 +1722,7 @@
     "plt.plot(x, logistic(x, -5, 7), label=r\"$\\beta = -5, \\alpha = 7$\",\n",
     "         color=\"#7A68A6\")\n",
     "\n",
+    "plt.title(\"Logistic functon with bias, plotted for several value of $\\\\alpha$ bias parameter\", fontsize=14)\n",
     "plt.legend(loc=\"lower left\");"
    ]
   },