- 2 A Let The Random Variables X And Y Have The Joint Distribution 0 X 0 Or Y 0 5 X E X 1 Y X 1 E X 0 X 4 1 1 (25.33 KiB) Viewed 26 times
u and variance o2. Find the following:
2. (a) Let the random variables X and Y have the joint distribution 0, x <0 or y < 0 5(x+e-(x+1)y² x+1 -e-x²), 0≤x <4 (1+²e-5y²e-y², 4 ≤ x and any y 20 Fxy(x, y) = (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 μ and variance o². Find the following: (i) E[(X-Y)²] (ii) E[(X+Y)²] (iii) Cov{(X+Y), (X-Y)}