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 Fxy(x, y)

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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 Fxy X Y 1 (31.33 KiB) Viewed 44 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 Fxy(x, y) = 5(x+o-(x+1)y² x+1 1+-e-5y²-e-y², -e-x²), (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 be independent and identically distributed random variables with me μ and variance a2. Find the following: (i) E[(X-Y)²] (ii) E[(X+Y)²] (iii) Cov{(X+Y), (X-Y)}