2. Suppose X and Y have the joint pdf fxy(x, y) = e-(x+y), 0 < x < 00, 0 < y < 0o, zero elsewhere. (a) Find the pdf of Z = X+Y. (b) Find the moment generating function of Z.
4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x < y < 1, and zero otherwise. (a) Find fx(x). (b) Find fy(y). (c) Find Corr(X,Y). (d) Find fy x(y|x). (e) Find E(Y|X). (f) Find Var(Y). (g) Find Var(E(Y|X)). (h) Find E (Var(Y|X)]. (i) Find the pdf of Y - X.
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
2. Let the random variables X and Y have the joint PDF given below: 2e -y 0 xyo0 fxy (x, y) otherwise 0 (a) Find P(X Y < 2) (b) Find the marginal PDFs of X and Y (c) Find the conditional PDF of Y X x (d) Find P(Y< 3|X = 1)
4) The random variables X and Y have the joint PDF fx,y(x, y) = 0 < x < 6,0 < y < 6 Find E [X2Y2].
2. Let the random variables X and Y have the joint PDF given below: S 2e-2-Y 0 < x < y < fxy(x,y) = { 0 otherwise (a) Find P(X+Y < 2). (b) Find the marginal PDFs of X and Y. (c) Find the conditional PDF of Y|X = r. (d) Find P(Y <3|X = 1).
Two random variables have joint PDF of F(x, y) = 0 for x < 0 and y < 0 for 0 <x< 1 and 0 <y<1 1. for x > 1 and y> 1 a) Find the joint and marginal pdfs. b) Use F(x, y) and find P(X<0.75, Y> 0.25), P(X<0.75, Y = 0.25), P(X<0.25)
Let X and Y have joint pdf f(x, y)= e if 0 < x < y< o and zero otherwise. Find Е(X |у). 16.
The joint pdf of X and Y is f(x,y)= { (1 + xy2) 0 < x < y < 1 otherwise. 0 Find E(X Y = y) 5y2 6 543 27 y2 + + cola 2 3y+2y4 3(73+2)
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y), 0 < y < x <1 otBerwise a. Find c. b. Find the joint pdf of S = Y and T = XY. c. Find the marginal pdf of T. 、