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Exercise 2: Suppose that the joint pdf of (X, Y)' is fx.y(r,y) = c(r + y), if r € 0,1, 2,3 %3D and y € 0, 1, 2, 3. a: What is the value of c? b: What are the marginal pdfs fx(x) and fy(y)? c: What is E(Y | X = 3) ?

Exercise 2: Suppose that the joint pdf of (X, Y)' is fx.y(r,y) = c(r + y), if r € 0,1, 2,3 %3D and y € 0, 1, 2, 3. a: What is the value of c? b: What are the marginal pdfs fx(x) and fy(y)? c: What is E(Y | X = 3) ?

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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Exercise 2: Suppose that the joint pdf of (X,Y) is fx.x(r, y) = c(r + y), if r E 0, 1,2, 3 and y € 0, 1, 2,3. a: What is the value of c? b: What are the marginal pdfs fx(r) and fy(y)? c: What is E(Y |X = 3) ? d: What is cov(3X – 5, Y)? Hint: Covariance is linear in each coordinate. That means two things. First, you can pass constants through either coordinate: Cov(aX, Y) = a Cov(X,Y) = Cov(X, aY) Second, it preserves sums in each coordinate: Cov (X1 + X2, Y) = Cov (X1, Y) + Cov (X2, Y) For example: if X2 = c, so X2 is a constant, then Cov (X1 + X2, Y) = Cov (X1, Y) + Cov (c, Y) = Cov (X1, Y)
Transcribed Image Text:Exercise 2: Suppose that the joint pdf of (X,Y) is fx.x(r, y) = c(r + y), if r E 0, 1,2, 3 and y € 0, 1, 2,3. a: What is the value of c? b: What are the marginal pdfs fx(r) and fy(y)? c: What is E(Y |X = 3) ? d: What is cov(3X – 5, Y)? Hint: Covariance is linear in each coordinate. That means two things. First, you can pass constants through either coordinate: Cov(aX, Y) = a Cov(X,Y) = Cov(X, aY) Second, it preserves sums in each coordinate: Cov (X1 + X2, Y) = Cov (X1, Y) + Cov (X2, Y) For example: if X2 = c, so X2 is a constant, then Cov (X1 + X2, Y) = Cov (X1, Y) + Cov (c, Y) = Cov (X1, Y)
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