{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": [
"remove_cell"
]
},
"outputs": [],
"source": [
"# HIDDEN\n",
"from datascience import *\n",
"from prob140 import *\n",
"import numpy as np\n",
"import warnings\n",
"import matplotlib.cbook\n",
"warnings.filterwarnings(\"ignore\",category=matplotlib.cbook.mplDeprecation)\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('fivethirtyeight')\n",
"%matplotlib inline\n",
"from scipy import stats"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"tags": [
"remove_cell"
]
},
"outputs": [],
"source": [
"# HIDDEN\n",
"\n",
"def sin(theta):\n",
" return np.sin(theta * np.pi/180)\n",
"def cos(theta):\n",
" return np.cos(theta * np.pi/180)\n",
"def tan(theta):\n",
" return sin(theta)/cos(theta)\n",
"\n",
"def projection_1_2(theta):\n",
" x = 1\n",
" z = 2\n",
" y = x*cos(theta) + z*sin(theta)\n",
" plt.figure(figsize=(6, 6))\n",
" plt.scatter(x, z, s=40, color='green')\n",
" plt.plot([-3, 3], [0, 0], color='grey', lw=2, label=r'$X$'+' axis')\n",
" plt.plot([0, 0], [-3, 3], color='grey', lw=2)\n",
" plt.plot([-3, 3], [tan(theta)*(-3), tan(theta)*3], color='gold', lw=2, label='New axis at positive angle '+r'$\\theta$ to the '+r'$X$'+' axis')\n",
" plt.plot([0, x], [0, 0], color='blue', lw=2)\n",
" plt.plot([x, x], [0, z], color='green', linestyle='--', lw=2)\n",
" plt.plot([x, cos(theta)*y], [z, sin(theta)*y], color='green', linestyle='--', lw=2)\n",
" plt.plot([0, cos(theta)*y], [0, sin(theta)*y], color='red', lw=2) \n",
" plt.gca().set_aspect('equal')\n",
" plt.legend(bbox_to_anchor=(1.92, 1.02))\n",
" plt.xlabel('$X$')\n",
" plt.ylabel('$Z$', rotation=0)\n",
" plt.title('Projection of $(X, Z) = (1, 2)$ on Gold Axis')\n",
" plt.xlim(-3, 3)\n",
" plt.ylim(-3, 3)\n",
" \n",
"def projection_trig():\n",
" x = 1\n",
" z = 2\n",
" x1 = x*cos(theta)\n",
" x2 = z*sin(theta)\n",
" y = x1 + x2\n",
" plt.figure(figsize=(8, 8))\n",
" plt.scatter(x, z, s=40, color='green')\n",
" plt.plot([-3, 3], [0, 0], color='grey', lw=2)\n",
" plt.plot([0, 0], [-3, 3], color='grey', lw=2)\n",
" plt.plot([-3, 3], [tan(theta)*(-3), tan(theta)*3], color='gold', lw=2)\n",
" plt.plot([0, x], [0, 0], color='blue', lw=2)\n",
" plt.plot([x, x], [0, z], color='green', linestyle='--', lw=2)\n",
" plt.plot([x, cos(theta)*y], [z, sin(theta)*y], color='green', linestyle='--', lw=2)\n",
" plt.plot([x, cos(theta)*x1], [0, sin(theta)*x1], color='k', linestyle='--', lw=2)\n",
" plt.plot([cos(theta)*y, x+cos(theta)*x2], [sin(theta)*y, sin(theta)*x2], color='k', linestyle='--', lw=2)\n",
" plt.plot([x, x+cos(theta)*x2], [0, sin(theta)*x2], color='k', linestyle='--', lw=2)\n",
" plt.plot([0, cos(theta)*x1], [0, sin(theta)*x1], color='brown', lw=3, label='Length = '+r'$X\\cos(\\theta)$')\n",
" plt.plot([cos(theta)*x1, cos(theta)*y], [sin(theta)*x1, sin(theta)*y], color='darkblue', lw=3, label='Length = '+r'$Z\\sin(\\theta)$')\n",
" plt.text(0.3, 0.06, r'$\\theta$', fontsize=20)\n",
" plt.text(1.03, 1.6, r'$\\theta$', fontsize=20)\n",
" plt.text(0.8, 2.1, r'$(X, Z)$', fontsize=15)\n",
" plt.legend(bbox_to_anchor=(1.35, 1))\n",
" plt.gca().set_aspect('equal')\n",
" plt.xlabel('$X$')\n",
" plt.ylabel('$Z$', rotation=0)\n",
" plt.title('$Y =$ '+r'$X\\cos(\\theta) + Z\\sin(\\theta)$')\n",
" plt.xlim(-0.5, 3)\n",
" plt.ylim(-0.5, 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Bivariate Normal Distribution ##"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When the joint distribution of $X$ and $Y$ is bivariate normal, the regression line of the previous section does even better than just being the best among all linear predictors of $Y$ based on $X$. In this section we will construct a bivariate normal pair $(X, Y)$ from i.i.d. standard normal variables. In the next section, we will identify the main property of the regression line for bivariate normal $(X, Y)$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The multivariate normal distribution is defined in terms of a mean vector and a covariance matrix. As you know, normalizing the covariance makes it is easier to interpret. You have shown in exercises that for jointly distributed random variables $X$ and $Y$ the *correlation* between $X$ and $Y$ is defined as\n",
"\n",
"$$\n",
"r_{X,Y} ~ = ~ \\frac{Cov(X, Y)}{\\sigma_X\\sigma_Y} ~ = ~ \n",
"E\\Big{(} \\frac{X-\\mu_X}{\\sigma_X} \\cdot \\frac{Y-\\mu_Y}{\\sigma_Y} \\Big{)}\n",
"~ = ~ E(X_{su}Y_{su})\n",
"$$\n",
"\n",
"where $X_{su}$ is $X$ in standard units and $Y_{su}$ is $Y$ in standard units.\n",
"\n",
"### Properties of Correlation ###\n",
"You showed all of these in exercises.\n",
"\n",
"- $r_{X,Y}$ depends only on standard units and hence is a pure number with no units\n",
"- $r_{X,Y} = r_{Y,X}$\n",
"- $-1 \\le r_{X,Y} \\le 1$ \n",
"- If $Y = aX + b$ then $r_{X,Y}$ is $1$ or $-1$ according to whether the sign of $a$ is positive or negative. \n",
"\n",
"We say that $r_{X,Y}$ measures the *linear association* between $X$ and $Y$. \n",
"\n",
"### Correlation as a Cosine ###\n",
"Rewrite the formula for correlation to see that \n",
"\n",
"$$\n",
"Cov(X, Y) ~ = ~ r_{X,Y}\\sigma_X\\sigma_Y\n",
"$$\n",
"\n",
"So the variance of $X+Y$ is\n",
"\n",
"$$\n",
"\\sigma_{X+Y}^2 ~ = ~ \\sigma_X^2 + \\sigma_Y^2 + 2r_{X,Y}\\sigma_X\\sigma_Y\n",
"$$\n",
"\n",
"Notice the parallel with the formula for the length of the sum of two vectors, with correlation playing the role of the cosine of the angle between two vectors. If the angle is 90 degrees, the the cosine is 0. This corresponds to correlation being zero and hence the random variables being uncorrelated. \n",
"\n",
"Later in this section, we will visualize this idea in the case where the joint distribution of $X$ and $Y$ is bivariate normal."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"tags": [
"remove-input",
"hide-output"
]
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" VIDEO \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# VIDEO: Construction: Bivariate Normal\n",
"from IPython.display import YouTubeVideo\n",
"\n",
"YouTubeVideo('d-ucYswhZ_Q')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"tags": [
"remove-input",
"hide-output"
]
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" VIDEO \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# VIDEO: Construction: Standard Bivariate Normal\n",
"\n",
"YouTubeVideo('GQ9nsyr3umI')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Constructing the Standard Bivariate Normal ###\n",
"\n",
"The goal is to construct $X$ and $Y$ that have the multivariate normal distribution with mean vector $[0 ~ 0]^T$ and covariance matrix \n",
"$\\begin{bmatrix}\n",
"1 & \\rho \\\\\n",
"\\rho & 1\n",
"\\end{bmatrix}$\n",
"for some $\\rho$ such that $0 < \\rho < 1$. We will say that $X$ and $Y$ have the *standard bivariate normal distribution with correlation $\\rho$*.\n",
"\n",
"Any bivariate normal vector is a linear transformation of an i.i.d. standard normal vector. Start with two i.i.d. standard normal random variables $X$ and $Z$. We will construct the required bivariate normal random vector $[X ~ Y]^T$ as a linear transformation of the random vector $[X ~ Z]^T$.\n",
"\n",
"First note that since all three of $X$, $Y$, and $Z$ must have mean $0$, the linear transformation has no shift term. We just need to identify numbers $a$, $b$, $c$, and $d$ such that\n",
"\n",
"$$\n",
"\\begin{bmatrix}\n",
"X \\\\\n",
"Y\n",
"\\end{bmatrix}\n",
"~ = ~\n",
"\\begin{bmatrix}\n",
"a & b \\\\\n",
"c & d\n",
"\\end{bmatrix}\n",
"\\begin{bmatrix}\n",
"X \\\\\n",
"Z\n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"Taking $a=1$ and $b=0$ is a good start because it gives us the right first coordinate.\n",
"\n",
"$$\n",
"\\begin{bmatrix}\n",
"1 & 0 \\\\\n",
"c & d\n",
"\\end{bmatrix}\n",
"\\begin{bmatrix}\n",
"X \\\\\n",
"Z\n",
"\\end{bmatrix}\n",
"~=~\n",
"\\begin{bmatrix}\n",
"X \\\\\n",
"cX+dZ\n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"Since both $X$ and $Y$ must have variance $1$, the covariance of $X$ and $Y$ is equal to the correlation. So, by the independence of $X$ and $Z$,\n",
"\n",
"$$\n",
"\\rho ~ = ~ Cov(X, cX+dZ) ~ = ~ cVar(X) = c\n",
"$$\n",
"\n",
"So now we have\n",
"\n",
"$$\n",
"\\begin{bmatrix}\n",
"1 & 0 \\\\\n",
"\\rho & d\n",
"\\end{bmatrix}\n",
"\\begin{bmatrix}\n",
"X \\\\\n",
"Z\n",
"\\end{bmatrix}\n",
"~=~\n",
"\\begin{bmatrix}\n",
"X \\\\\n",
"\\rho X+dZ\n",
"\\end{bmatrix}\n",
"~ = ~ \n",
"\\begin{bmatrix}\n",
"X \\\\\n",
"Y\n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"Since $Var(Y) = 1$, the final condition is $1 = Var(\\rho X + dZ) = \\rho^2Var(X) + d^2Var(Z) = rho^2 + d^2$. So $d = \\sqrt{1 - \\rho^2}$ will work, and we have the following result.\n",
"\n",
"- Let $X$ be standard normal.\n",
"- Let $Z$ be standard normal, independent of $X$.\n",
"- Let $Y = \\rho X + \\sqrt{1-\\rho^2}Z$. \n",
"- Then $X$ and $Y$ have the standard bivariate normal distribution with correlation $\\rho$.\n",
"\n",
"It is also true that if $X$ and $Y$ are standard bivariate normal with correlation $\\rho$, then there is a standard normal $Z$ independent of $X$ such that $Y = \\rho X + \\sqrt{1-\\rho^2}Z$. The proof is an exercise.\n",
"\n",
"The graph below shows the empirical distribution of 1000 $(X, Y)$ points in the case $\\rho = 0.6$. You can change the value of $rho$ and see how the scatter diagram changes. It will remind you of numerous such simulations in Data 8."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plotting parameters\n",
"plt.figure(figsize=(5, 5))\n",
"plt.axes().set_aspect('equal')\n",
"plt.xlabel('$X$')\n",
"plt.ylabel('$Y$', rotation=0)\n",
"plt.xticks(np.arange(-4, 4.1))\n",
"plt.yticks(np.arange(-4, 4.1))\n",
"\n",
"# X, Z, and Y\n",
"x = stats.norm.rvs(0, 1, size=1000)\n",
"z = stats.norm.rvs(0, 1, size=1000)\n",
"rho = 0.6\n",
"y = rho*x + np.sqrt((1-rho**2))*z\n",
"plt.scatter(x, y, color='darkblue', s=10);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Representations of the Bivariate Normal ###\n",
"\n",
"When we are working with just two variables $X$ and $Y$, matrix representations are usually unnecessary. We will use the following three representations interchangeably.\n",
"\n",
"- $X$ and $Y$ are bivariate normal with parameters $(\\mu_X, \\mu_Y, \\sigma_X^2, \\sigma_Y^2, \\rho)$\n",
"- The standardized variables $X_{su}$ and $Y_{su}$ are standard bivariate normal with correlation $\\rho$. Then $Y_{su} = \\rho X_{su} + \\sqrt{1-\\rho^2}Z$ for some standard normal $Z$ that is independent of $X_{su}$. This follows from Definition 2 of the multivariate normal.\n",
"- $X$ and $Y$ have the multivariate normal distribution with mean vector $[\\mu_X ~ \\mu_Y]^T$ and covariance matrix\n",
"\n",
"$$\n",
"\\begin{bmatrix}\n",
"\\sigma_X^2 & \\rho\\sigma_X\\sigma_Y \\\\\n",
"\\rho\\sigma_X\\sigma_Y & \\sigma_Y^2\n",
"\\end{bmatrix}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Standard Bivariate Normal: Matrix Approach ###\n",
"In lab, you used a matrix approach to constructing standard bivariate normal $X$ and $Y$ with correlation $\\rho$. Here is a summary of the construction. The end result is the same as what we developed above.\n",
"\n",
"Let $X$ and $Z$ be independent standard normal variables, that is, bivariate normal random variables with mean vector $\\mathbf{0}$ and covariance matrix equal to the identity. Now fix a number $\\rho$ (that's the Greek letter rho, the lower case r) so that $-1 < \\rho < 1$, and let\n",
"\n",
"$$\n",
"\\mathbf{A} ~ = ~ \n",
"\\begin{bmatrix}\n",
"1 & 0 \\\\\n",
"\\rho & \\sqrt{1 - \\rho^2}\n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"Define a new random variable $Y = \\rho X + \\sqrt{1-\\rho^2}Z$, and notice that\n",
"\n",
"$$\n",
"\\begin{bmatrix}\n",
"X \\\\\n",
"Y\n",
"\\end{bmatrix} \n",
"~ = ~\n",
"\\begin{bmatrix}\n",
"1 & 0 \\\\\n",
"\\rho & \\sqrt{1 - \\rho^2}\n",
"\\end{bmatrix}\n",
"\\begin{bmatrix}\n",
"X \\\\\n",
"Z\n",
"\\end{bmatrix}\n",
"~ = ~ \n",
"\\mathbf{A}\n",
"\\begin{bmatrix}\n",
"X \\\\\n",
"Z\n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"So $X$ and $Y$ have the bivariate normal distribution with mean vector $\\mathbf{0}$ and covariance matrix\n",
"\n",
"$$\n",
"\\mathbf{AIA}^T ~ = ~ \n",
"\\begin{bmatrix}\n",
"1 & 0 \\\\\n",
"\\rho & \\sqrt{1 - \\rho^2}\n",
"\\end{bmatrix}\n",
"\\begin{bmatrix}\n",
"1 & \\rho \\\\\n",
"0 & \\sqrt{1 - \\rho^2}\n",
"\\end{bmatrix}\n",
"~ = ~ \n",
"\\begin{bmatrix}\n",
"1 & \\rho \\\\\n",
"\\rho & 1\n",
"\\end{bmatrix}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Correlation as a Cosine: Geometry in the Bivariate Normal Case ###\n",
"We have defined\n",
"\n",
"$$\n",
"Y ~ = ~ \\rho X + \\sqrt{1 - \\rho^2} Z\n",
"$$\n",
"where $X$ and $Z$ are i.i.d. standard normal.\n",
"\n",
"Let's understand this construction geometrically. A good place to start is the joint density of $X$ and $Z$, which has circular symmetry."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"tags": [
"remove_input"
]
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# NO CODE\n",
"\n",
"Plot_bivariate_normal([0, 0], [[1, 0], [0, 1]])\n",
"plt.xlabel('$X$')\n",
"plt.ylabel('$Z$')\n",
"plt.gca().set_zlabel('$f(x, z)$')\n",
"plt.title('Standard Bivariate Normal Distribution, Correlation = 0');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The $X$ and $Z$ axes are orthogonal. Let's see what happens if we twist them. \n",
"\n",
"Take any positive angle $\\theta$ degrees and draw a new axis at angle $\\theta$ to the original $X$ axis. Every point $(X, Z)$ has a *projection* onto this axis. \n",
"\n",
"The figure below shows the projection of the point $(X, Z) = (1, 2)$ onto the gold axis which is at an angle of $\\theta$ degress to the $X$ axis. The blue segment is the value of $X$. You get that by dropping the perpendicular from $(1, 2)$ to the horizontal axis. That's called *projecting* $(1, 2)$ onto the horizontal axis. \n",
"\n",
"The red segment is the projection of $(1, 2)$ onto the gold axes, obtained by dropping the perpendicular from $(1, 2)$ to the gold axis.\n",
"\n",
"Vary the values of $\\theta$ in the cell below to see how the projection changes as the gold axis rotates."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"theta = 20\n",
"projection_1_2(theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let $Y$ be the length of the red segment, and remember that $X$ is the length of the blue segment. When $\\theta$ is very small, $Y$ is almost equal to $X$. When $\\theta$ approaches 90 degrees, $Y$ is almost equal to $Z$.\n",
"\n",
"A little trigonometry shows that $Y ~ = ~ X \\cos(\\theta) + Z\\sin(\\theta)$."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"projection_trig()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Thus\n",
"\n",
"$$\n",
"Y ~ = ~ X\\cos(\\theta) + Z\\sin(\\theta) ~ = ~ \\rho X + \\sqrt{1 - \\rho^2}Z\n",
"$$\n",
"\n",
"where $\\rho = \\cos(\\theta)$.\n",
"\n",
"The sequence of graphs below illustrates the transformation for $\\theta = 30$ degrees."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"theta = 30\n",
"projection_1_2(theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The bivariate normal distribution is the joint distribution of the blue and red lengths $X$ and $Y$ when the original point $(X, Z)$ has i.i.d. standard normal coordinates. This transforms the circular contours of the joint density surface of $(X, Z)$ into the elliptical contours of the joint density surface of $(X, Y)$. "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.8660254037844387, 0.8660254037844386)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cos(theta), (3**0.5)/2"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"rho = cos(theta)\n",
"Plot_bivariate_normal([0, 0], [[1, rho], [rho, 1]])\n",
"plt.title('Standard Bivariate Normal Distribution, Correlation = '+str(round(rho, 2)));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Small $\\theta$ ###\n",
"\n",
"As we observed earlier, when $\\theta$ is very small there is hardly any change in the position of the axis. So $X$ and $Y$ are almost equal. "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"theta = 2\n",
"projection_1_2(theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The bivariate normal density of $X$ and $Y$, therefore, is essentially confined to the $X = Y$ line. The correlation $\\cos(\\theta)$ is large because $\\theta$ is small; it is more than 0.999. \n",
"\n",
"You can see the plotting function having trouble rendering this joint density surface."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.99939082701909576"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rho = cos(theta)\n",
"rho"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Plot_bivariate_normal([0, 0], [[1, rho], [rho, 1]])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Orthogonality and Independence ###\n",
"When $\\theta$ is 90 degrees, the gold axis is orthogonal to the $X$ axis and $Y$ is equal to $Z$ which is independent of $X$."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"theta = 90\n",
"projection_1_2(theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When $\\theta = 90$ degrees, $\\cos(\\theta) = 0$. The joint density surface of $(X, Y)$ is the same as that of $(X, Z)$ and has circular symmetry."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you think of $\\rho X$ as a \"signal\" and $\\sqrt{1-\\rho^2}Z$ as \"noise\", then $Y$ can be thought of as an observation whose value is \"signal plus noise\". In the rest of the chapter we will see if we can separate the signal from the noise."
]
}
],
"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": "3.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 4
}