The random variables X and Y have joint density function f(x, y) = 2-1.2x -0.8y, 0≤x≤1, 0≤y≤1. Calculate the covariance of X and Y as Cov(X, Y) = E[(X — Hx)(Y — HY)] = S¹ S² (2 − [x)(y − &Y)f(2,3)dyda Note: You will have to first calculate ux and μy as μχ 1 : E[X] = ₁²₁² a f(x, y)dyda, and = My = E[Y] = 1 Syf(x, y) dydz
The random variables X and Y have joint density function f(x, y) = 2-1.2x -0.8y, 0≤x≤1, 0≤y≤1. Calculate the covariance of X and Y as Cov(X, Y) = E[(X — Hx)(Y — HY)] = S¹ S² (2 − [x)(y − &Y)f(2,3)dyda Note: You will have to first calculate ux and μy as μχ 1 : E[X] = ₁²₁² a f(x, y)dyda, and = My = E[Y] = 1 Syf(x, y) dydz
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![The random variables \(X\) and \(Y\) have joint density function
\[
f(x, y) = 2 - 1.2x - 0.8y, \quad 0 \leq x \leq 1, \, 0 \leq y \leq 1.
\]
Calculate the covariance of \(X\) and \(Y\) as
\[
\text{Cov}(X, Y) = E\left[(X - \mu_X)(Y - \mu_Y)\right] = \int_0^1 \int_0^1 (x - \mu_X)(y - \mu_Y)f(x, y)\,dy\,dx = \,
\]
Note: You will have to first calculate \(\mu_X\) and \(\mu_Y\) as
\[
\mu_X = E[X] = \int_0^1 \int_0^1 x f(x, y)\,dy\,dx,
\]
and
\[
\mu_Y = E[Y] = \int_0^1 \int_0^1 y f(x, y)\,dy\,dx.
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Transcribed Image Text:The random variables \(X\) and \(Y\) have joint density function
\[
f(x, y) = 2 - 1.2x - 0.8y, \quad 0 \leq x \leq 1, \, 0 \leq y \leq 1.
\]
Calculate the covariance of \(X\) and \(Y\) as
\[
\text{Cov}(X, Y) = E\left[(X - \mu_X)(Y - \mu_Y)\right] = \int_0^1 \int_0^1 (x - \mu_X)(y - \mu_Y)f(x, y)\,dy\,dx = \,
\]
Note: You will have to first calculate \(\mu_X\) and \(\mu_Y\) as
\[
\mu_X = E[X] = \int_0^1 \int_0^1 x f(x, y)\,dy\,dx,
\]
and
\[
\mu_Y = E[Y] = \int_0^1 \int_0^1 y f(x, y)\,dy\,dx.
\]
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