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5. Random variables X and Y have the joint PDF shown below: -1.0 y 2.0 1.0 -1.0 -2.0 1.0 fxy(x, y) = 0.1 20 (a) Find the conditional PDFs fyx (yl) and fxy (ly). (b) Find E[X|Y=y], E[X], and Var(X Y = y). Use these to calculate Var(X). (c) Find E[Y|X=2], E[Y], and Var(Y|X= z). Use these to calculate Var(Y).

5. Random variables X and Y have the joint PDF shown below: -1.0 y 2.0 1.0 -1.0 -2.0 1.0 fxy(x, y) = 0.1 20 (a) Find the conditional PDFs fyx (yl) and fxy (ly). (b) Find E[X|Y=y], E[X], and Var(X Y = y). Use these to calculate Var(X). (c) Find E[Y|X=2], E[Y], and Var(Y|X= z). Use these to calculate Var(Y).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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5. Random variables X and Y have the joint PDF shown below: -1.0 y 2.0 1.0 -1.0 -2.0 1.0 fxy(x, y) = 0.1 20 (a) Find the conditional PDFs fyx (yl) and fxy (ay). (b) Find E[X|Y=y], E[X], and Var(X|Y= y). Use these to calculate Var(X). (c) Find E[Y|X = x], E[Y], and Var(Y|X = z). Use these to calculate Var(Y).
Transcribed Image Text:5. Random variables X and Y have the joint PDF shown below: -1.0 y 2.0 1.0 -1.0 -2.0 1.0 fxy(x, y) = 0.1 20 (a) Find the conditional PDFs fyx (yl) and fxy (ay). (b) Find E[X|Y=y], E[X], and Var(X|Y= y). Use these to calculate Var(X). (c) Find E[Y|X = x], E[Y], and Var(Y|X = z). Use these to calculate Var(Y).
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