probVectors.ipynb

{
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   "source": [
    "# Probability, Random Vectors, and the Multivariate Normal Distribution"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## Probability\n",
    "\n",
    "This course assumes that you have already had an introduction to probability, random variables, expectation, and so on, so the treatment is very cursory.\n",
    "The treatment is quite informal, omitting important technical concepts such as sigma-algebras,\n",
    "measurability, and the like.\n",
    "\n",
    "Modern probability theory starts with Kolmogorov's Axioms; here is an informal startement of the axioms.\n",
    "For more (but still a very informal treatment), see these chapters of SticiGui: \n",
    "[Probability: Philosophy and Mathematical Background](http://www.stat.berkeley.edu/~stark/SticiGui/Text/probabilityPhilosophy.htm),\n",
    "[Set theory](http://www.stat.berkeley.edu/~stark/SticiGui/Text/sets.htm),\n",
    "and\n",
    "[Probability: Axioms and Fundaments](http://www.stat.berkeley.edu/~stark/SticiGui/Text/probabilityAxioms.htm).\n",
    "\n",
    "Let $S$ denote the _outcome space_, the set of all possible outcomes of a random experiment, \n",
    "and let $\\{A_i\\}_{i=1}^\\infty$ be subsets of $S$.\n",
    "(Note that here $A$ denotes a subset, not a matrix.)\n",
    "Then any probability function ${\\mathbb P}$ must satisfy these axioms:\n",
    "\n",
    "1. For every $A \\subset S$, ${\\mathbb P}(A) \\ge 0$ (probabilities are nonnegative)\n",
    "2. ${\\mathbb P}(S) = 1$ (the chance that _something_ happens is 100%)\n",
    "3. If $A_i \\cap A_j = \\emptyset$ for $i \\ne j$, then ${\\mathbb P} \\cup_{i=1}^\\infty A_i = \\sum_{i=1}^\\infty {\\mathbb P}(A_i)$\n",
    "(If a countable collection of events is _pairwise disjoint_, then the chance that any of the\n",
    "events occurs is the sum of the chances that they occur individually.)\n",
    "\n",
    "These axioms have many useful consequences, among them that ${\\mathbb P}(\\emptyset) = 0$, ${\\mathbb P}(A^c) = 1 - {\\mathbb P}(A)$,\n",
    "and ${\\mathbb P}(A \\cup B) = {\\mathbb P}(A) + {\\mathbb P}(B) - {\\mathbb P}(AB)$.\n",
    "\n",
    "---\n",
    "### Definitions\n",
    "\n",
    "Let $A$ and $B$ be subsets of outcome space $S$.\n",
    "\n",
    "+ If $AB = \\emptyset$, then $A$ and $B$ are _mutually exclusive_.\n",
    "+ If ${\\mathbb P}(AB) = {\\mathbb P}(A){\\mathbb P}(B)$, then $A$ and $B$ are _independent_.\n",
    "+ If ${\\mathbb P}(B) > 0$, then the _conditional probability of $A$ given $B$_ is\n",
    "${\\mathbb P}(A | B) \\equiv {\\mathbb P}(AB)/{\\mathbb P}(B)$.\n",
    "---\n",
    "\n",
    "Independence is an extremely specific relationship.\n",
    "At one extreme, $AB = \\emptyset$; then ${\\mathbb P}(AB) = 0 \\le {\\mathbb P}(A){\\mathbb P}(B)$. \n",
    "At another extreme, either $A$ is a subset of $B$ or vice versa; then ${\\mathbb P}(AB) = \\min({\\mathbb P}(A),{\\mathbb P}(B)) \\ge {\\mathbb P}(A){\\mathbb P}(B)$.\n",
    "Independence lies at a precise point in between."
   ]
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    "## Random variables\n",
    "\n",
    "Briefly, a _real-valued random variable_ $X$ can be characterized by its probability distribution, which specifies (for a suitable collection of subsets of the real line $\\Re$ that comprises a sigma-algebra), the chance that the value of $X$ will be in each such subset.\n",
    "There are technical requirements regarding  _measurability_, which generally we will ignore.\n",
    "Perhaps the most natural mathematical setting for probability theory involves _Lebesgue integration_;\n",
    "we will largely ignore the difference between a _Riemann integral_ and a _Lebesgue integral_.\n",
    "\n",
    "Let $P_X$ denote the probability distribution of the random variable $X$. \n",
    "Then if $A \\subset \\Re$, $P_X(A) = {\\mathbb P} \\{ X \\in A \\}$.\n",
    "We write $X \\sim P_X$,\n",
    "pronounced \"$X$ is distributed as $P_X$\" or \"$X$ has distribution $P_X$.\" \n",
    "\n",
    "If two random variables $X$ and $Y$ have the same distribution, we write $X \\sim Y$ and we say that $X$ and $Y$\n",
    "are _identically distributed_.\n",
    "\n",
    "Real-valued random variables can be _continuous_, _discrete_, or _mixed (general)_.\n",
    "\n",
    "Continuous random variables have _probability density functions_ with respect to Lebesgue measure.\n",
    "If $X$ is a continuous random variables, there is some nonnegative function $f(x)$,\n",
    "the probability density of $X$, such that\n",
    "for any (suitable) set $A \\subset \\Re$,\n",
    "\\begin{equation*} \n",
    "  {\\mathbb P} \\{ X \\in A \\} = \\int_A f(x) dx.\n",
    "\\end{equation*}\n",
    "Since ${\\mathbb P} \\{ X \\in \\Re \\} = 1$, it follows that $\\int_{-\\infty}^\\infty f(x) dx = 1$.\n",
    "\n",
    "_Example._ \n",
    "Let $f(x) = \\lambda e^{-\\lambda x}$ for $x \\ge 0$, and $f(x) = 0$ otherwise.\n",
    "Clearly $f(x) \\ge 0$.\n",
    "\\begin{equation*} \n",
    "  \\int_{-\\infty}^\\infty f(x) dx = \\int_0^\\infty \\lambda e^{-\\lambda x} dx\n",
    "  = - e^{-\\lambda x}|_0^\\infty = - 0 + 1 = 1.\n",
    "\\end{equation*}\n",
    "Hence, $\\lambda e^{-\\lambda x}$ can be the probability density of a continuous random variable.\n",
    "A random variable with this density is said to be _exponentially distributed_.\n",
    "Exponentially distributed random variables are used to model radioactive decay and the failure\n",
    "of items that do not \"fatigue.\" For instance, the lifetime of a semiconductor after an initial\n",
    "\"burn-in\" period is often modeled as an exponentially distributed random variable.\n",
    "It is also a common model for the occurrence of earthquakes (although it does not fit the data well).\n",
    "\n",
    "_Example._\n",
    "Let $a$ and $b$ be real numbers with $a < b$, and let $f(x) = \\frac{1}{b-a}$, $x \\in [a, b]$ and \n",
    "$f(x)=0$, otherwise. \n",
    "Then $f(x) \\ge 0$ and $\\int_{-\\infty}^\\infty f(x) dx = \\int_a^b \\frac{1}{b-a} = 1$,\n",
    "so $f(x)$ can be the probability density function of a continuous random variable.\n",
    "A random variable with this density is sad to be _uniformly distributed on the interval $[a, b]$_.\n",
    "\n",
    "Discrete random variables assign all their probability to some _countable_ set of points $\\{x_i\\}_{i=1}^n$,\n",
    "where $n$ might be infinite.\n",
    "Discrete random variables have _probability mass functions_.\n",
    "If $X$ is a discrete random variable, there is a nonnegative function $p$, the probability mass function\n",
    "of $X$, such that\n",
    "for any set $A \\subset \\Re$,\n",
    "\\begin{equation*} \n",
    "  {\\mathbb P} \\{X \\in A \\} = \\sum_{i: x_i \\in A} p(x_i).\n",
    "\\end{equation*}\n",
    "The value $p(x_i) = {\\mathbb P} \\{X = x_i\\}$, and $\\sum_{i=1}^\\infty p(x_i) = 1$.\n",
    "\n",
    "_Example._\n",
    "Let $x_i = i-1$ for $i=1, 2, \\ldots$, and let $p(x_i) = e^{-\\lambda} \\lambda^{x_i}/x_i!$.\n",
    "Then $p(x_i) > 0$ and \n",
    "\\begin{equation*}  \n",
    "\\sum_{i=1}^\\infty p(x_i) = e^{-\\lambda} \\sum_{j=0}^\\infty \\lambda^j/j! = e^{-\\lambda} e^{\\lambda} = 1.\n",
    "\\end{equation*}\n",
    "Hence, $p(x)$ is the probability mass function of a discrete random variable.\n",
    "A random variable with this probability mass function is said to be _Poisson distributed (with parameter\n",
    "$\\lambda$)_.\n",
    "Poisson-distributed random variables are often used to model rare events.\n",
    "\n",
    "\n",
    "_Example._\n",
    "Let $x_i = i$ for $i=1, \\ldots, n$, and let $p(x_i) = 1/n$ and $p(x) = 0$, otherwise.\n",
    "Then $p(x) \\ge 0$ and $\\sum_{x_i} p(x_i) = 1$.\n",
    "Hence, $p(x)$ can be the probability mass function of a discrete random variable.\n",
    "A random variable with this probability mass function is said to be _uniformly distributed on $1, \\ldots, n$_.\n",
    "\n",
    "_Example._\n",
    "Let $x_i = i-1$ for $i=1, \\ldots, n+1$, and let $p(x_i) = {n \\choose x_i} p^{x_i} (1-p)^{n-x_i}$, and\n",
    "$p(x) = 0$ otherwise.\n",
    "Then $p(x) \\ge 0$ and \n",
    "\\begin{equation*} \n",
    "\\sum_{x_i} p(x_i) = \\sum_{j=0}^n {n \\choose j} p^j (1-p)^{n-j} = 1,\n",
    "\\end{equation*}\n",
    "by the binomial theorem.\n",
    "Hence $p(x)$ is the probability mass function of a discrete random variable.\n",
    "A random variable with this probability mass function is said to be _binomially distributed\n",
    "with parameters $n$ and $p$_.\n",
    "The number of successes in $n$ independent trials that each have the same probability $p$ of success\n",
    "has a binomial distribution with parameters $n$ and $p$\n",
    "For instance, the number of times a fair die lands with 3 spots showing in 10 independent rolls has\n",
    "a binomial distribution with parameters $n=10$ and $p = 1/6$.\n",
    "\n",
    "For general random variables, the chance that $X$ is in some subset of $\\Re$ cannot be written as\n",
    "a sum or as a Riemann integral; it is more naturally represented as a Lebesgue integral (with respect to\n",
    "a measure other than Lebesgue measure).\n",
    "For example, imagine a random variable $X$ that has probability $\\alpha$ of being equal to zero;\n",
    "and if $X$ is not zero, it has a uniform distribution on the interval $[0, 1]$.\n",
    "Such a random variable is neither continuous nor discrete.\n",
    "\n",
    "Most of the random variables in this class are either discrete or continuous.\n",
    "\n",
    "If $X$ is a random variable such that, for some constant $x_1 \\in \\Re$, ${\\mathbb P}(X = x_1) = 1$, $X$\n",
    "is called a _constant random variable_.\n"
   ]
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    "### Exercises\n",
    "\n",
    "+ Show analytically that $\\sum_{x_i} p(x_i) = \\sum_{j=0}^n {n \\choose j} p^j (1-p)^{n-j} = 1$.\n",
    "+ Write an R script that verifies that equation numerically for $n=10$: for 1000 values of $p$ \n",
    "equispaced on the interval $(0, 1)$, find the maximum absolute value of the difference between the sum and 1.\n",
    "+ Let $ \\in (0, 1]$; let $x_i = 1, 2, \\ldots$; and define $p(x_i) = (1-p)^{x_i-1}p$, and $p(x) = 0$ otherwise. Show analytically that $p(x)$ is the probability mass function of a discrete random variable. \n",
    "(A random variable with this probability mass function is said to be _geometrically distributed\n",
    "with parameter $p$_.)\n",
    "+ Starting from Kolmogorov's three axioms, show that ${\\mathbb P}(A \\cup B) = {\\mathbb P}(A) + {\\mathbb P}(B) - {\\mathbb P}(AB)$.\n",
    "+ Starting from Kolmogorov's three axioms, show that \n",
    "${\\mathbb P}(A \\cup B \\cup C) = {\\mathbb P}(A) + {\\mathbb P}(B) + {\\mathbb P}(C) - {\\mathbb P}(AB) - {\\mathbb P}(AC) - {\\mathbb P}(BC) + {\\mathbb P}(ABC)$.\n",
    "+ Starting from Kolmogorov's three axioms, show that ${\\mathbb P}(AB) \\le \\min({\\mathbb P}(A),{\\mathbb P}(B))$."
   ]
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    "## Jointly Distributed Random Variables\n",
    "\n",
    "Often we work with more than one random variable at a time.\n",
    "Indeed, much of this course concerns _random vectors_, the components of which are individual\n",
    "real-valued random variables.\n",
    "\n",
    "The _joint probability distribution_ of a collection of random variables $\\{X_i\\}_{i=1}^n$ gives the probability that\n",
    "the variables simultaneously fall in subsets of their possible values.\n",
    "That is, for every (suitable) subset $ A \\in \\Re^n$, the joint probability distribution of $\\{X_i\\}_{i=1}^n$\n",
    "gives ${\\mathbb P} \\{ (X_1, \\ldots, X_n) \\in A \\}$.\n",
    "\n",
    "An _event determined by the random variable $X$_ is an event of the form $X \\in A$, where $A \\subset \\Re$.\n",
    "\n",
    "An _event determined by the random variables $\\{X_j\\}_{j \\in J}$_ is an event of the form\n",
    "$(X_j)_{j \\in J} \\in A$, where $A \\subset \\Re^{\\#J}$.\n",
    "\n",
    "Two random variables $X_1$ and $X_2$ are _independent_ if every event determined by $X_1$ is independent\n",
    "of every event determined by $X_2$.\n",
    "If two random variables are not independent, they are _dependent_.\n",
    "\n",
    "A collection of random variables $\\{X_i\\}_{i=1}^n$ is _independent_ if every event determined by every subset\n",
    "of those variables is independent of every event determined by any disjoint subset of those variables.\n",
    "If a collection of random variables is not independent, it is _dependent_.\n",
    "\n",
    "Loosely speaking, a collection of random variables is independent if learning the values of some of them\n",
    "tells you nothing about the values of the rest of them.\n",
    "If learning the values of some of them tells you anything about the values of the rest of them,\n",
    "the collection is dependent.\n",
    "\n",
    "For instance, imagine tossing a fair coin twice and rolling a fair die.\n",
    "Let $X_1$ be the number of times the coin lands heads, and $X_2$ be the number of spots that show on the die.\n",
    "Then $X_1$ and $X_2$ are independent: learning how many times the coin lands heads tells you nothing about what\n",
    "the die did.\n",
    "\n",
    "On the other hand, let $X_1$ be the number of times the coin lands heads, and let $X_2$ be the sum of the\n",
    "number of heads and the number of spots that show on the die.\n",
    "Then $X_1$ and $X_2$ are dependent. For instance, if you know the coin landed heads twice, you know that the sum\n",
    "of the number of heads and the number of spots must be at least 3."
   ]
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    "## Expectation\n",
    "\n",
    "See [SticiGui: The Long Run and the Expected Value](http://www.stat.berkeley.edu/~stark/SticiGui/Text/expectation.htm) for an elementary introduction to expectation.\n",
    "\n",
    "The _expectation_ or _expected value_ of a random variable $X$, denoted ${\\mathbb E}X$, is a probability-weighted average of its possible values.\n",
    "From a frequentist perspective, it is the long-run limit (in probabiity) of the average of its values in repeated experiments.\n",
    "The expected value of a real-valued random variable (when it exists) is a fixed number, not a random value.\n",
    "The expected value depends on the probability distribution of $X$ but not on any realized value of $X$.\n",
    "If two random variables have the same probability distribution, they have the same expected value.\n",
    "\n",
    "---\n",
    "### Properties of Expectation\n",
    "\n",
    "+ For any real $\\alpha \\in \\Re$, if ${\\mathbb P} \\{X = \\alpha\\} = 1$, then ${\\mathbb E}X = \\alpha$: the expected\n",
    "value of a constant random variable is that constant.\n",
    "+ For any real $\\alpha \\in \\Re$, ${\\mathbb E}(\\alpha X) = \\alpha {\\mathbb E}X$: scalar homogeneity.\n",
    "+ If $X$ and $Y$ are random variables, ${\\mathbb E}(X+Y) = {\\mathbb E}X + {\\mathbb E}Y$: additivity.\n",
    "---\n",
    "\n",
    "### Calculating Expectation\n",
    "If $X$ is a continuous real-valued random variable with density $f(x)$, then the expected value of $X$ is\n",
    "\\begin{equation*} \n",
    "   {\\mathbb E}X = \\int_{-\\infty}^\\infty x f(x) dx,\n",
    "\\end{equation*}\n",
    "provided the integral exists.\n",
    "\n",
    "_Example._\n",
    "Suppose $X$ has density $f(x) = \\frac{1}{b-a}$ for $a \\le x \\le b$ and $0$ otherwise.\n",
    "Then $ {\\mathbb E}X = \\int_{-\\infty}^\\infty x f(x) dx = \\frac{1}{b-a} \\int_a^b x dx = \\frac{b^2-a^2}{2(b-a)} =\n",
    "\\frac{a+b}{2}$.\n",
    "\n",
    "If $X$ is a discrete real-valued random variable with probability function $p$, then the expected value of $X$ is\n",
    "\\begin{equation*} \n",
    "   {\\mathbb E}X = \\sum_{i=1}^\\infty x_i p(x_i),\n",
    "\\end{equation*}\n",
    "where $\\{x_i\\} = \\{ x \\in \\Re: p(x) > 0\\}$,\n",
    "provided the sum exists.\n",
    "\n",
    "_Example._\n",
    "Suppose $X$ has a Poisson distribution with parameter $\\lambda$.\n",
    "Then ${\\mathbb E}X = e^{-\\lambda} \\sum_{j=0}^\\infty j \\lambda^j/j! = \\lambda$."
   ]
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    "## Variance,  Standard Error, and Covariance\n",
    "\n",
    "See [SticiGui: Standard Error](http://www.stat.berkeley.edu/~stark/SticiGui/Text/standardError.htm) for an elementary introduction to variance and standard error.\n",
    "\n",
    "The _variance_ of a random variable $X$ is $\\mbox{Var }X = {\\mathbb E}(X - {\\mathbb E}X)^2$.\n",
    "\n",
    "Algebraically, the following identity holds:\n",
    "\\begin{equation*} \n",
    "\\mbox{Var } X = {\\mathbb E}(X - {\\mathbb E}X)^2 = {\\mathbb E}X^2 - 2({\\mathbb E}X)^2 + ({\\mathbb E}X)^2 =\n",
    "{\\mathbb E}X^2 - ({\\mathbb E}X)^2.\n",
    "\\end{equation*}\n",
    "However, this is generally not a good way to calculate $\\mbox{Var} X$ numerically, because of roundoff:\n",
    "it sacrifices precision unnecessarily.\n",
    "\n",
    "The _standard error_ of a random variable $X$ is $\\mbox{SE }X = \\sqrt{\\mbox{Var } X}$.\n",
    "\n",
    "If $\\{X_i\\}_{i=1}^n$ are independent, then $\\mbox{Var} \\sum_{i=1}^n X_i = \\sum_{i=1}^n \\mbox{Var }X_i$.\n",
    "\n",
    "If $X$ and $Y$ have a joint distribution, then $\\mbox{cov} (X,Y) = {\\mathbb E} (X - {\\mathbb E}X)(Y - {\\mathbb E}Y)$.\n",
    "It follows from this definition (and the commutativity of multiplication)\n",
    "that $\\mbox{cov}(X,Y) = \\mbox{cov}(Y,X)$.\n",
    "Also,\n",
    "\\begin{equation*} \n",
    "\\mbox{var }(X+Y) = \\mbox{var }X + \\mbox{var }Y + 2\\mbox{cov}(X,Y).\n",
    "\\end{equation*}\n",
    "\n",
    "If $X$ and $Y$ are independent, $\\mbox{cov }(X,Y) = 0$. \n",
    "However, the converse is not necessarily true: $\\mbox{cov}(X,Y) = 0$ does not in general imply that\n",
    "$X$ and $Y$ are independent."
   ]
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    "## Random Vectors\n",
    "\n",
    "Suppose $\\{X_i\\}_{i=1}^n$ are jointly distributed random variables, and let\n",
    "\\begin{equation*} \n",
    "X = \n",
    "\\begin{pmatrix}\n",
    "X_1 \\\\\n",
    "\\vdots \\\\\n",
    "X_n\n",
    "\\end{pmatrix}\n",
    ".\n",
    "\\end{equation*}\n",
    "Then $X$ is a random vector, a $n$ by $1$ vector of real-valued random variables.\n",
    "\n",
    "The expected value of $X$ is\n",
    "\\begin{equation*} \n",
    "{\\mathbb E} X =\n",
    "\\begin{pmatrix}\n",
    "{\\mathbb E} X_1 \\\\\n",
    "\\vdots \\\\\n",
    "{\\mathbb E} X_n\n",
    "\\end{pmatrix}\n",
    ".\n",
    "\\end{equation*}\n",
    "\n",
    "The _covariance matrix_ of $X$ is\n",
    "\\begin{equation*} \n",
    "\\mbox{cov } X = \n",
    "{\\mathbb E} \n",
    "\\left (\n",
    "\\begin{pmatrix}\n",
    "X_1 - {\\mathbb E} X_1 \\\\\n",
    "\\vdots \\\\\n",
    "X_n - {\\mathbb E} X_n\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}\n",
    "X_1 - {\\mathbb E} X_1 & \\cdots & X_n - {\\mathbb E} X_n\n",
    "\\end{pmatrix}\n",
    "\\right )\n",
    "=\n",
    "{\\mathbb E} \n",
    "\\begin{pmatrix}\n",
    "(X_1 - {\\mathbb E} X_1)^2 & (X_1 - {\\mathbb E} X_1)(X_2 - {\\mathbb E} X_2) & \\cdots & (X_1 - {\\mathbb E} X_1)(X_n - {\\mathbb E} X_n) \\\\\n",
    "(X_1 - {\\mathbb E} X_1)(X_2 - {\\mathbb E} X_2) & (X_2 - {\\mathbb E} X_2)^2 & \\cdots & (X_2 - {\\mathbb E} X_2)(X_n - {\\mathbb E} X_n) \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "(X_1 - {\\mathbb E} X_1)(X_n - {\\mathbb E} X_n) & (X_2 - {\\mathbb E} X_2)(X_n - {\\mathbb E} X_n) & \\cdots & (X_n - {\\mathbb E} X_n)^2\n",
    "\\end{pmatrix}\n",
    "\\end{equation*}\n",
    "\n",
    "\\begin{equation*} \n",
    "= \n",
    "\\begin{pmatrix}\n",
    "{\\mathbb E}(X_1 - {\\mathbb E} X_1)^2 & {\\mathbb E}((X_1 - {\\mathbb E} X_1)(X_2 - {\\mathbb E} X_2)) & \\cdots & \n",
    "{\\mathbb E}(X_1 - {\\mathbb E} X_1)(X_n - {\\mathbb E} X_n)) \\\\\n",
    "{\\mathbb E}((X_1 - {\\mathbb E} X_1)(X_2 - {\\mathbb E} X_2)) & {\\mathbb E}(X_2 - {\\mathbb E} X_2)^2 & \\cdots & \n",
    "{\\mathbb E}((X_2 - {\\mathbb E} X_2)(X_n - {\\mathbb E} X_n)) \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "{\\mathbb E}((X_1 - {\\mathbb E} X_1)(X_n - {\\mathbb E} X_n)) & {\\mathbb E}(X_2 - {\\mathbb E} X_2)(X_n - {\\mathbb E} X_n)) & \\cdots & {\\mathbb E}(X_n - {\\mathbb E} X_n)^2\n",
    "\\end{pmatrix}\n",
    ".\n",
    "\\end{equation*}\n",
    "\n",
    "Covariance matrices are always _positive semidefinite_.\n"
   ]
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    "## The Multivariate Normal Distribution\n",
    "\n",
    "The notation $X \\sim {\\mathcal N}(\\mu, \\sigma^2)$ means that $X$ has a normal distribution with mean $\\mu$\n",
    "and variance $\\sigma^2$.\n",
    "This distribution is continuous, with probability density function\n",
    "\\begin{equation*} \n",
    "\\frac{1}{\\sqrt{2\\pi} \\sigma} e^{\\frac{-(x-\\mu)^2}{2\\sigma^2}}.\n",
    "\\end{equation*}\n",
    "\n",
    "If $X \\sim {\\mathcal N}(\\mu, \\sigma^2)$, then $\\frac{X-\\mu}{\\sigma} \\sim {\\mathcal N}(0, 1)$,\n",
    "the _standard normal distribution_.\n",
    "The probability density function of the standard normal distribution is\n",
    "\\begin{equation*} \n",
    "\\phi(x) = \\frac{1}{\\sqrt{2\\pi}} e^ {-x^2/2}.\n",
    "\\end{equation*}\n",
    "\n"
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      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "\n",
       "\n"
      ],
      "text/plain": [
       "numeric(0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": 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",
      "text/plain": [
       "Plot with title “The Standard Normal Curve”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plot the normal density\n",
    "x <- seq(from = -5, to = 5, by=0.01);\n",
    "y <- (2*pi)^(-1/2)*exp(-x^2/2);\n",
    "plot(x,y, type = \"n\") +\n",
    "abline(h = 0) +\n",
    "lines(x,y) +\n",
    "title(main = \"The Standard Normal Curve\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A collection of random variables $\\{ X_1, X_2, \\ldots, X_n\\} = \\{X_j\\}_{j=1}^n$ is _jointly normal_\n",
    "if all linear combinations of those variables have normal distributions.\n",
    "That is, the collection is jointly normal if for all $\\alpha \\in \\Re^n$, $\\sum_{j=1}^n \\alpha_j X_j$\n",
    "has a normal distribution.\n",
    "\n",
    "If $\\{X_j \\}_{j=1}^n$ are independent, normally distributed random variables, they are jointly normal.\n",
    "\n",
    "If for some $\\mu \\in \\Re^n$ and positive-definite matrix $G$, the joint density of $\\{X_j \\}_{j=1}^n$ is\n",
    "\\begin{equation*}  \n",
    "\\left ( \\frac{1}{\\sqrt{2 \\pi}}\\right )^n \\frac{1}{\\sqrt{\\left | G \\right |}} \n",
    "\\exp \\left \\{ - \\frac{1}{2} (x - \\mu)'G^{-1}(x-\\mu) \\right \\},\n",
    "\\end{equation*}\n",
    "then $\\{X_j \\}_{j=1}^n$ are jointly normal, and the covariance matrix of $\\{X_j\\}_{j=1}^n$ is $G$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example\n",
    "[TO DO!]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Central Limit Theorem\n",
    "\n",
    "For an elementary discussion, see [SticiGui: The Normal Curve, The Central Limit Theorem, and Markov's and Chebychev's Inequalities for Random Variables](http://www.stat.berkeley.edu/~stark/SticiGui/Text/clt.htm).\n",
    "\n",
    "Suppose $\\{X_j \\}_{j=1}^\\infty$ are independent and identically distributed (iid), have finite expected value ${\\mathbb E}X_j = \\mu$, and have finite variance $\\mbox{var }X_j = \\sigma^2$.\n",
    "\n",
    "Define the sum $S_n \\equiv \\sum_{j=1}^n X_j$.\n",
    "Then \n",
    "\\begin{equation*} \n",
    "{\\mathbb E}S_n = {\\mathbb E} \\sum_{j=1}^n X_j = \\sum_{j=1}^n {\\mathbb E} X_j = \\sum_{j=1}^n \\mu = n\\mu,\n",
    "\\end{equation*}\n",
    "and\n",
    "\\begin{equation*} \n",
    "\\mbox{var }S_n = \\mbox{var } \\sum_{j=1}^n X_j = n\\sigma^2.\n",
    "\\end{equation*}\n",
    "(The last step follows from the independence of $\\{X_j\\}$: the variance of the sum is the sum of the variances.)\n",
    "\n",
    "Define $Z_n \\equiv \\frac{S_n - n\\mu}{\\sqrt{n}\\sigma}$.\n",
    "Then for every $a, b \\in \\Re$ with $a \\le b$,\n",
    "\\begin{equation*} \n",
    "\\lim_{n \\rightarrow \\infty} {\\mathbb P} \\{ a \\le Z_n \\le b \\} = \\frac{1}{\\sqrt{2\\pi}} \\int_a^b e^{-x^2/2} dx.\n",
    "\\end{equation*}\n",
    "This is a basic form of the Central Limit Theorem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability Inequalities and Identities\n",
    "This follows Lugosi (2006) rather closely; it's also a repeat of the results in the chapter on \n",
    "[Mathematical Preliminaries](mathPrelim.ipynb), which we largely omitted.\n",
    "\n",
    "#### The tail-integral formula for expectation\n",
    "If $X$ is a nonnegative real-valued random variable,\n",
    "\\begin{equation*} \n",
    "{\\mathbb E} X = \\int_0^\\infty {\\mathbb P} \\{X \\ge x\\} dx\n",
    "\\end{equation*}\n",
    "\n",
    "#### Jensen's Inequality\n",
    "If $\\phi$ is a convex function from ${\\mathcal X}$ to $\\Re$, then $\\phi({\\mathbb E} X) \\le {\\mathbb E} \\phi(X)$.\n",
    "\n",
    "#### Markov's, Chebychev's, and related inequalities\n",
    "From the tail-integral formula,\n",
    "\\begin{equation*} \n",
    "{\\mathbb E} X \\ge \\int_0^t {\\mathbb P} \\{X \\ge x\\} dx \\ge t {\\mathbb P} \\{X \\ge t \\},\n",
    "\\end{equation*}\n",
    "which yields _Markov's Inequality_:\n",
    "\\begin{equation*} \n",
    "{\\mathbb P} \\{ X \\ge t \\} \\le \\frac{{\\mathbb E} X}{t}.\n",
    "\\end{equation*}\n",
    "\n",
    "Moreover, for any strictly monotonic function $f$ and nonnegative $X$,\n",
    "we have the _Generalized Markov Inequality_:\n",
    "\\begin{equation*} \n",
    "{\\mathbb P} \\{ X \\ge t \\} = {\\mathbb P} \\{ f(X) \\ge f(t) \\} \\le \\frac{{\\mathbb E} f(X)}{f(t)}.\n",
    "\\end{equation*}\n",
    "In particular, for any real-valued $X$ and real $q > 0$,\n",
    "$| X - {\\mathbb E} X |$ is a nonnegative\n",
    "random variable and $f(x) = x^q$ is strictly monotonic, so\n",
    "\\begin{equation*} \n",
    "{\\mathbb P} \\{| X - {\\mathbb E} X | \\ge t \\} = {\\mathbb P} \\{ | X - {\\mathbb E} X |^q \\ge t^q \\} \\le\n",
    "\\frac{{\\mathbb E}  | X - {\\mathbb E} X |^q}{t^q}.\n",
    "\\end{equation*}\n",
    "_Chebychev's inequality_ is a special case:\n",
    "\\begin{equation*} \n",
    "{\\mathbb P} \\{ | X - {\\mathbb E} X |^2 \\ge t^2 \\} \\le \\frac{{\\mathbb E}  | X - {\\mathbb E} X |^2}{t^2}\n",
    "= \\frac{{\\mbox{Var}} X}{t^2}.\n",
    "\\end{equation*}\n",
    "\n",
    "#### The Chernoff Bound\n",
    "Apply the Generalized Markov Inequality with $f(x) = e^{sx}$ for positive $s$\n",
    "to obtain the _Chernoff Bound_:\n",
    "\\begin{equation*} \n",
    "{\\mathbb P} \\{ X \\ge t \\} = {\\mathbb P} \\{ e^{sX} \\ge e^{st} \\} \\le \\frac{{\\mathbb E} e^{sX}}{e^{st}}\n",
    "\\end{equation*}\n",
    "for all $s$.\n",
    "For particular $X$, one can optimize over $s$.\n",
    "\n",
    "\n",
    "#### Hoeffding's Inequality\n",
    "Let $\\{ X_j \\}_{j=1}^n$ be independent, and define\n",
    "$S_n \\equiv \\sum_{j=1}^n X_j$.\n",
    "Applying the Chernoff Bound yields\n",
    "\\begin{equation*} \n",
    "{\\mathbb P} \\{ S_n - {\\mathbb E} S_n \\ge t \\} \\le e^{-st} {\\mathbb E} e^{sS_n} =\n",
    "e^{-st} \\prod_{j=1}^n e^{s(X_j - E X_j)}.\n",
    "\\end{equation*}\n",
    "Hoeffding bounds the moment generating function for a bounded random variable\n",
    "$X$:\n",
    "If $a \\le X \\le b$ with probability 1, then\n",
    "\\begin{equation*} \n",
    "{\\mathbb E} e^{sX}  \\le e^{s^2 (b-a)^2/8},\n",
    "\\end{equation*}\n",
    "from which follows _Hoeffding's tail bound_.\n",
    "\n",
    "If $\\{X_j\\}_{j=1}^n$ are independent and ${\\mathbb P} \\{a_j \\le X_j \\le b_j\\} = 1$,\n",
    "then\n",
    "\\begin{equation*}  \n",
    "{\\mathbb P} \\{ S_n - {\\mathbb E} S_n \\ge t \\} \\le e^{-2t^2/\\sum_{j=1}^n (b_j - a_j)^2}\n",
    "\\end{equation*}\n",
    "and\n",
    "\\begin{equation*}  \n",
    "{\\mathbb P} \\{ S_n - {\\mathbb E} S_n \\le -t \\} \\le e^{-2t^2/\\sum_{j=1}^n (b_j - a_j)^2}\n",
    "\\end{equation*}\n",
    "\n",
    "#### Hoeffding's Other Inequality\n",
    "Suppose $f$ is a convex, real function and ${\\mathcal X}$ is a finite set.\n",
    "Let $\\{X_j \\}_{j=1}^n$ be a simple random sample from ${\\mathcal X}$ and\n",
    "let $\\{Y_j \\}_{j=1}^n$ be an iid uniform random sample (with replacement) from ${\\mathcal X}$.\n",
    "Then\n",
    "\\begin{equation*}   \n",
    "{\\mathbb E} f \\left ( \\sum_{j=1}^n X_j \\right ) \\le {\\mathbb E} f \\left ( \\sum_{j=1}^n Y_j \\right ).\n",
    "\\end{equation*}\n",
    "\n",
    "#### Bernstein's Inequality\n",
    "Suppose $\\{X_j \\}_{j=1}^n$ are independent with ${\\mathbb E} X_j = 0$ for all $j$,\n",
    "${\\mathbb P} \\{ | X_j | \\le c\\} = 1$,\n",
    "$\\sigma_j^2 = {\\mathbb E} X_j^2$ and $\\sigma = \\frac{1}{n} \\sum_{j=1}^n \\sigma_j^2$.\n",
    "Then for any $\\epsilon > 0$,\n",
    "\\begin{equation*} \n",
    "{\\mathbb P} \\{ S_n/n > \\epsilon \\} \\le e^{-n \\epsilon^2 / 2(\\sigma^2 + c\\epsilon/3)}.\n",
    "\\end{equation*}"
   ]
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