2. (a) Let the random variables X and Y have the joint distribution 0, x <0 or y < 0 0

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2 A Let The Random Variables X And Y Have The Joint Distribution 0 X 0 Or Y 0 0 X 4 4 X And Any Y 20 Fxr X Y 1 (24.98 KiB) Viewed 5 times

2. (a) Let the random variables X and Y have the joint distribution 0, x <0 or y < 0 0<x<4 4 ≤ x and any y 20 Fxr(x, y) = (x+-+²-e-x²). (1+²e-5y²e-², (i) Find the marginal distributions Fx (x) and Fy (y). (ii) Compute the joint probability P(3 < X < 5,1 <Y ≤ 2). (iii) Compute the conditional probability P(3 < X < 51 <Y ≤ 2) (b) Let X and Y be independent and identically distributed random variables with mean and variance a². Find the following: (1) E[(X-Y)²] (ii) E[(X+Y)²] (iii) Cov((X+Y). (X-Y)}