Thank You So Much

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Thank You So Much

Thank You So Much 1 (49.01 KiB) Viewed 105 times

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2. (a) Let the random variables X and Y have the joint distribution 0, x<0 or y<0 5/x+6 (x+1)2 ( -- e-x²). 0≤x≤4 x+1 (1 + ²e-³y² - e-v². 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)}