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 ≥ 0 Fxx (

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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 0 Fxx 1 (50.07 KiB) Viewed 8 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 ≥ 0 Fxx (x, y) = SI+ x+e-(x+1)y² x+1 5 (1 + ²1/e-5y². -~-x²), e-y², (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 <≤ 5|1 < Y ≤ 2) (b) Let X and Y be independent and identically distributed random variables with mean u and variance o2. Find the following: (i) E[(X - Y)²] (ii) E[(X + Y)²] (iii) Cov{(X+Y), (X — Y)}