{
"cells": [
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"tags": [
"remove_cell"
]
},
"outputs": [],
"source": [
"# HIDDEN\n",
"from datascience import *\n",
"from prob140 import *\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('fivethirtyeight')\n",
"%matplotlib inline\n",
"import math\n",
"from scipy import stats\n",
"from sympy import *\n",
"init_printing()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Independence ##"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Informally, the definition of independence is the same as before: two random variables that have a joint density are independent if additional information about one of them doesn't change the distribution of the other.\n",
"\n",
"One quick way to spot the lack of independence is to look at the set of possible values of the pair $(X, Y)$. If that set is not a rectangle then $X$ and $Y$ can't be independent. The non-rectangular shape implies that there must be two values of $X$ for which the corresponding values of $Y$ are different."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{admonition} Quick Check\n",
"The \"unit disc\" is the disc of radius 1 centered at the origin. That is, it's the set of points $(x,y)$ such that $x^2 + y^2 \\le 1$. Suppose the joint density of $X$ and $Y$ is positive on the unit disc and $0$ elsewhere. Pick the correct option.\n",
"\n",
"(i) It is not possible to determine whether or not $X$ and $Y$ are independent.\n",
"\n",
"(ii) $X$ and $Y$ are independent.\n",
"\n",
"(iii) $X$ and $Y$ are not independent.\n",
"\n",
"\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{admonition} Answer\n",
":class: dropdown\n",
"(iii)\n",
"\n",
"\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": [
"remove-input",
"hide-output"
]
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" VIDEO"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# VIDEO\n",
"from IPython.display import YouTubeVideo\n",
"\n",
"YouTubeVideo('jVHgjZBMYq0')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the set of possible values is rectangular then you have to check independence using the old definition:\n",
"\n",
"Jointly distributed random variables $X$ and $Y$ are *independent* if\n",
"\n",
"$$\n",
"P(X \\in A, Y \\in B) = P(X \\in A)P(Y \\in B)\n",
"$$\n",
"\n",
"for all intervals $A$ and $B$.\n",
"\n",
"Let $X$ have density $f_X$, let $Y$ have density $f_Y$, and suppose $X$ and $Y$ are independent. Then if $f$ is the joint density of $X$ and $Y$,\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"f(x, y)dxdy &\\sim P(X \\in dx, Y \\in dy) \\\\\n",
"&= P(X \\in dx)P(Y \\in dy) ~~~~~ \\text{(independence)} \\\\\n",
"&= f_X(x)dx f_Y(y)dy \\\\\n",
"&= f_X(x)f_Y(y)dxdy\n",
"\\end{align*}\n",
"$$\n",
"\n",
"Thus if $X$ and $Y$ are independent then their joint density is given by\n",
"\n",
"$$\n",
"f(x, y) = f_X(x)f_Y(y)\n",
"$$\n",
"\n",
"This is the *product rule for densities*: the joint density of two independent random variables is the product of their densities.\n",
"\n",
"The converse is also true: if the joint density factors into a function of $x$ times a function of $y$, then $X$ and $Y$ are independent."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Independent Standard Normal Random Variables ###\n",
"Suppose $X$ and $Y$ are i.i.d. standard normal random variables. Then their joint density is given by\n",
"\n",
"$$\n",
"f(x, y) = \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{1}{2}x^2} \\cdot \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{1}{2}y^2}, ~~~~ -\\infty < x, y < \\infty\n",
"$$\n",
"\n",
"Equivalently,\n",
"$$\n",
"f(x, y) = \\frac{1}{2\\pi} e^{-\\frac{1}{2}(x^2 + y^2)}, ~~~~ -\\infty < x, y < \\infty\n",
"$$\n",
"\n",
"Here is a graph of the joint density surface."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def indep_standard_normals(x,y):\n",
" return 1/(2*math.pi) * np.exp(-0.5*(x**2 + y**2))\n",
"\n",
"Plot_3d((-4, 4), (-4, 4), indep_standard_normals, rstride=4, cstride=4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice the circular symmetry of the surface. This is because the formula for the joint density involves the pair $(x, y)$ through the expression $x^2 + y^2$ which is symmetric in $x$ and $y$.\n",
"\n",
"Notice also that $P(X = Y) = 0$, as the probability is the volume over a line. This is true of all pairs of independent random variables with a joint density: $P(X = Y) = 0$. So for example $P(X > Y) = P(X \\ge Y)$. You don't have to worry about whether or not to the inequality should be strict."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{admonition} Quick Check\n",
"$X$ is normal $(0, 4)$ and $Y$ is normal $(0, 9)$. Suppose $X$ and $Y$ are independent. Find the joint density of $X$ and $Y$.\n",
"\n",
"\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{admonition} Answer\n",
":class: dropdown\n",
"$f(x,y) = \\frac{1}{\\sqrt{2\\pi}\\cdot2} e^{-\\frac{1}{2}\\cdot\\frac{x^2}{4}} \\cdot \\frac{1}{\\sqrt{2\\pi}\\cdot3} e^{-\\frac{1}{2}\\cdot\\frac{y^2}{9}}$\n",
"for all $x, y$\n",
"\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{admonition} Quick Check\n",
"For some positive constant $c$, the random variables $X$ and $Y$ have joint density $f(x,y) = ce^{-\\frac{1}{10}(x^2+y^2)}$ for all $x$ and $y$. Are $X$ and $Y$ independent?\n",
"\n",
"\n",
"\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{admonition} Answer\n",
":class: dropdown\n",
"Yes\n",
"\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Competing Exponentials ###\n",
"\n",
"Let $X$ and $Y$ be independent random variables. Suppose $X$ has the exponential $(\\lambda)$ distribution and $Y$ has the exponential $(\\mu)$ distribution. The goal of this example is to find $P(Y > X)$.\n",
"\n",
"By the product rule, the joint density of $X$ and $Y$ is given by\n",
"\n",
"$$\n",
"f(x, y) ~ = ~ \\lambda e^{-\\lambda x} \\mu e^{-\\mu y}, ~~~~ x > 0, ~ y > 0\n",
"$$\n",
"\n",
"The graph below shows the joint density surface in the case $\\lambda = 0.5$ and $\\mu = 0.25$, so that $E(X) = 2$ and $E(Y) = 4$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def independent_exp(x, y):\n",
" return 0.5 * 0.25 * np.e**(-0.5*x - 0.25*y)\n",
"\n",
"Plot_3d((0, 10), (0, 10), independent_exp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To find $P(Y > X)$ we must integrate the joint density over the upper triangle of the first quadrant, a portion of which is shown below."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"tags": [
"remove_input"
]
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# NO CODE\n",
"plt.axes().set_aspect('equal')\n",
"xx = np.arange(0, 10.1, 0.1)\n",
"yy = 10*np.ones(len(xx))\n",
"plt.fill_between(xx, xx, yy, alpha=0.3)\n",
"plt.xlabel('$x$')\n",
"plt.ylabel('$y$', rotation=0)\n",
"plt.title('$Y > X$ (portion of infinite region)');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The probability is therefore\n",
"$$\n",
"P(Y > X) ~ = ~ \\int_0^\\infty \\int_x^\\infty \\lambda e^{-\\lambda x} \\mu e^{-\\mu y} dy dx\n",
"$$\n",
"\n",
"We can do this double integral without much calculus, just by using probability facts. As you calculate, try to involve densities as much as possible, and remember that the integral of a density over an interval is the probability of that interval.\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"P(Y > X) &= \\int_0^\\infty \\int_x^\\infty \\lambda e^{-\\lambda x} \\mu e^{-\\mu y} dy dx \\\\ \\\\\n",
"&= \\int_0^\\infty \\lambda e^{-\\lambda x} \\big{(} \\int_x^\\infty \\mu e^{-\\mu y} dy\\big{)} dx \\\\ \\\\\n",
"&= \\int_0^\\infty \\lambda e^{-\\lambda x} e^{-\\mu x} dx ~~~~~~ \\text{(survival function of } Y\\text{, evaluated at } x \\text{)} \\\\ \\\\\n",
"&= \\frac{\\lambda}{\\lambda + \\mu} \\int_0^\\infty (\\lambda + \\mu) e^{-(\\lambda + \\mu)x} dx \\\\ \\\\\n",
"&= \\frac{\\lambda}{\\lambda + \\mu} ~~~~~~~ \\text{(total integral of exponential }\n",
"(\\lambda + \\mu) \\text{ density is 1)}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"Thus\n",
"\n",
"$$\n",
"P(Y > X) ~ = ~ \\frac{\\lambda}{\\lambda + \\mu}\n",
"$$\n",
"\n",
"Analogously,\n",
"\n",
"$$\n",
"P(X > Y) ~ = ~ \\frac{\\mu}{\\lambda + \\mu}\n",
"$$\n",
"\n",
"Notice that the two chances are proportional to the parameters. This is consistent with intuition if you think of $X$ and $Y$ as two lifetimes. If $\\lambda$ is large, the corresponding lifetime $X$ is likely to be short, and therefore $Y$ is likely to be larger than $X$ as the formula implies.\n",
"\n",
"If $\\lambda = \\mu$ then $P(Y > X) = 1/2$ which you can see by symmetry since $P(X = Y) = 0$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{admonition} Quick Check\n",
"The lifetimes of two electrical components are independent. The lifetime of Component 1 has the exponential $(0.1)$ distribution, and the lifetime of Component 2 has the exponential $(0.2)$ distribution.\n",
"\n",
"Without calculation, pick the correct option: The chance that Component 1 lives longer than Component 2 is\n",
"\n",
"(i) greater than $1/2$\n",
"\n",
"(ii) equal to $1/2$\n",
"\n",
"(iii) less than $1/2$\n",
"\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{admonition} Answer\n",
":class: dropdown\n",
"(i)\n",
"\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{admonition} Quick Check\n",
"Find the chance in Quick Check above.\n",
"\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"```{admonition} Answer\n",
":class: dropdown\n",
"$2/3$\n",
"\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we had attempted the double integral in the other order – first $x$, then $y$ – we would have had to do more work. The integral is\n",
"\n",
"$$\n",
"P(Y > X) ~ = ~ \\int_0^\\infty \\int_0^y \\lambda e^{-\\lambda x} \\mu e^{-\\mu y} dx dy\n",
"$$\n",
"\n",
"Let's take the easy way out by using `SymPy` to confirm that we will get the same answer."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"# Create the symbols; they are all positive\n",
"\n",
"x = Symbol('x', positive=True)\n",
"y = Symbol('y', positive=True)\n",
"lamda = Symbol('lamda', positive=True)\n",
"mu = Symbol('mu', positive=True)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$\\lambda \\mu e^{- \\lambda x} e^{- \\mu y}$$"
],
"text/plain": [
" -λ⋅x -μ⋅y\n",
"λ⋅μ⋅ℯ ⋅ℯ "
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Construct the expression for the joint density\n",
"\n",
"f_X = lamda * exp(-lamda * x)\n",
"f_Y = mu * exp(-mu * y)\n",
"joint_density = f_X * f_Y\n",
"joint_density"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$$\\int_{0}^{\\infty}\\int_{0}^{y} \\lambda \\mu e^{- \\lambda x} e^{- \\mu y}\\, dx\\, dy$$"
],
"text/plain": [
"∞ y \n",
"⌠ ⌠ \n",
"⎮ ⎮ -λ⋅x -μ⋅y \n",
"⎮ ⎮ λ⋅μ⋅ℯ ⋅ℯ dx dy\n",
"⌡ ⌡ \n",
"0 0 "
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Display the integral – first x, then y\n",
"\n",
"Integral(joint_density, (x, 0, y), (y, 0, oo))"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAHsAAAAuBAMAAAD6qnsIAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAzRAiu5mrdu/dZjKJVEQJ2sCdAAACaklEQVRIDd1WPWgUQRR+t5vNubf3q6SwW/AQrJIiCGJx18SUikWqgGcjQQKm0ZS5zkKMpxhRBNmApM0JFlp5FiJ2hyCWprKwSTgLCRr1vZnZ252dt2awEl8x773vZ3dmZ3bvAKziBcANKyEvegewwTNW6BQ4B1ZCVoTeyohlrED0enUrJSvyeuAPZljKBvTb0BoObJSsZroHl84OWcoG/LS4WnybIzyag6fgy6k6U85a7MjNjCdpmwuH293viT5bFQ+3V3tZU9Jb2BOxWf0Hduf4I4y7fVxc7Zd17AH8u2sPdsydipEVWfxp8s9jLZM/C8xb2r/KkBLi36ZTMDkEKEe5NkV4aoIZ3SbU+gjdy8Dj9mRHlq0Qc4EGLZahRf11DUw1zg/ZvMHkng9TjCifwFPK4hpZTvRLEr0N4MxdC5XkhMrOCJap9iMFGGkXHw1AIF7ltVDRH1WujNyD91h7bQUY6YhgSl0iDLu3sboVIVHs4sBGWdxX/jIYdl9MDaAqRJzf/UboRJtGwz4dEoxry/2EOfvEFzo0GvZnhGK4P2U2x+YanQv/AjGGXbzOe2jP+811j9XImb7760bjYaMxRdeLI/fuZ/peF0VpO7bxxkGzgx2u/atIxhCsQ0ATm2wTZUweHLnovCf/KgK4j0a5saYdrtBlQR4LUWrDPHbbM2pjF+48iCQ7njzshoTknzqph3WVZUrs/gohBTFqEr1Z1Nov467cozI+PmM4W+C/OTZOi/O2xXIpkL5JTAT1c4Q+ZigNcupaGzcvQ3p2pUHc5+YPHFO9Jb4UsxynYxVu9hM7UMJnd1GX/lX3G9z3rPcePDRmAAAAAElFTkSuQmCC\n",
"text/latex": [
"$$1 - \\frac{\\mu}{\\lambda \\left(1 + \\frac{\\mu}{\\lambda}\\right)}$$"
],
"text/plain": [
" μ \n",
"1 - ─────────\n",
" ⎛ μ⎞\n",
" λ⋅⎜1 + ─⎟\n",
" ⎝ λ⎠"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Evaluate the integral\n",
"\n",
"answer = Integral(joint_density, (x, 0, y), (y, 0, oo)).doit()\n",
"answer"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAADIAAAAvBAMAAABTWYTHAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKuJ70RUuyJ23TLNmWb8I+xeAAABK0lEQVQ4EWNgQAAhBQQblcX4GZWPxFNBYqMy4xNQ+QgeSwGCjcpi/ojKR/A4fiLYqCzGX6h8BE98/gYEB5nFcYL/AjIfwe7awOuA4CGxuF0ZuL8h8RHM/Q8YGJYjuEisSiD7fQOSwIhh/scFBkMIMCrhdIW8AS4pJgeoDGMDlAGjWGHJgm0CTAhGu0MZmDL2AhApuMwWBoZJYKF+qClwGSsGhrVgGfkFaHrOMjCC7Was/I0qAxRmA+eknoa/QBnmM2dO+Zw5cwHIBArzHgDSHKsZrgApIIDZw7uAgcuggYFhSwDD/gSQBFyGq4ChP8GAgfsfAwOQiSwDdNH97gQGdqCT+X6gyORfnslpCRaBETB7dGACcJr1AYTpCRdBY3BAvYcmDOSyLgASDAwARZBVMuvqu4EAAAAASUVORK5CYII=\n",
"text/latex": [
"$$\\frac{\\lambda}{\\lambda + \\mu}$$"
],
"text/plain": [
" λ \n",
"─────\n",
"λ + μ"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Confirm that it is the same \n",
"# as what we got by integrating in the other order\n",
"\n",
"simplify(answer)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"anaconda-cloud": {},
"celltoolbar": "Tags",
"kernelspec": {
"display_name": "Python 3",
"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": "3.8.3"
}
},
"nbformat": 4,
"nbformat_minor": 1
}