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(x, y) = C, for 0 < r < 1, and -I< y < % (1) Determine the value of C. (2) Find the marginal PDF of X. (3) Find the conditional PDF of Y given X = x. (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.
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(x, y) = C, for 0 < r < 1, and -I< y < % (1) Determine the value of C. (2) Find the marginal PDF of X. (3) Find the conditional PDF of Y given X = x. (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.
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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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(T,y) = C, for 0 < x < 1, and
– 1 < y< x
(1) Determine the value of C.
1.
(2) Find the marginal PDF of X.
(3) Find the conditional PDF of Y given X = x.
(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.
-1-
(6) Are X and Y independent or not? Justify your answer.
frod andY
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