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) Determine the value of C. ) Find the marginal PDF of X. -) Find the conditional PDF of Y given X = x.

) Determine the value of C. ) Find the marginal PDF of X. -) Find the conditional PDF of Y given X = x.

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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1. Random variables X and Y are uniformly distributed over region T enclosed by a triangle displayed by the shade in the right picture. A joint PDF of (X,Y)' up to a unknown constant C is given by f (r, y) = C, for 0 <x < 1, and – x < y< x y (1) Determine the value of C. (2) Find the marginal PDF of X. (3) Find the conditional PDF of Y given X = r. (4) Find E(Y|X), and V(Y|X). (5) Find the correlation coefficient Cor(X,Y). Hint: E(Y|X) is a linear function of X. (6) Are X and Y independent or not? Justify your answer.
Transcribed Image Text:1. Random variables X and Y are uniformly distributed over region T enclosed by a triangle displayed by the shade in the right picture. A joint PDF of (X,Y)' up to a unknown constant C is given by f (r, y) = C, for 0 <x < 1, and – x < y< x y (1) Determine the value of C. (2) Find the marginal PDF of X. (3) Find the conditional PDF of Y given X = r. (4) Find E(Y|X), and V(Y|X). (5) Find the correlation coefficient Cor(X,Y). Hint: E(Y|X) is a linear function of X. (6) Are X and Y independent or not? Justify your answer.
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