(a) Let X and Y be two jointly continuous random variables with joint probability density function r+ y 0

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Question 4
(a) Let X and Y be two jointly continuous random variables with joint probability density
function
r+y 0<r < 1 and 0 < y < 1
f(r, y) =
otherwise
Find the correlation coefficient p(X, Y).
0, Var(X;)
i = 1,2, 3, and Cov(X;, X;) = -0.5 for i + j. Let Y = E-iXi. Determine Var(Y).
(b) Suppose that X1, X2 and X3 are random variables with E(X;)
= 1 for
%3D
(c) Let X ~
Poi(X) and E(Y|X = x) = 1+
I+1
Use the law of total expectation to find
E(Y).
Transcribed Image Text:Question 4 (a) Let X and Y be two jointly continuous random variables with joint probability density function r+y 0<r < 1 and 0 < y < 1 f(r, y) = otherwise Find the correlation coefficient p(X, Y). 0, Var(X;) i = 1,2, 3, and Cov(X;, X;) = -0.5 for i + j. Let Y = E-iXi. Determine Var(Y). (b) Suppose that X1, X2 and X3 are random variables with E(X;) = 1 for %3D (c) Let X ~ Poi(X) and E(Y|X = x) = 1+ I+1 Use the law of total expectation to find E(Y).
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