6-x-4, 0x<2 0 1 2cych Exri If for two R.V. s X&Y the joint pdf is...
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)
The joint pdf of X and Y is given by f(x, y) = C,0<x<y<1. a) Determine the value of C. b) Determine the marginal distribution of X and compute E(X) and Var(X). c) Determine the marginal distribution of Y and compute E(Y) and Var(Y). d) Compute the correlation coefficient between X and Y.
4. Two RVs with a joint pdf given as follows fx.x ), 0<x< 1,0 <y<1 otherwise (a) Find fr ). (6 point) (b) Find fxy(x[y). (6 points) (c) Are X and Y independent? (clearly show justification for credit) (6 points)
Given f(x,y) = 2 ; 0 <X<y< 1 a. Prove that f(x,y) is a joint pdf b. Find the correlation coefficient of X and Y
Let X and Y be random variables with joint PDF fx,y(x, y) = 2 for 0 < y < x < 1. Find Var(Y|X).
1. Suppose X and Y are continuous random variables with joint pdf f(x,y) 4(z-xy) if = 0 < x < 1 and 0 < y < 1, and zero otherwise. (a) Find E(XY) b) Find E(X-Y) (c) Find Var(X - Y) (d) What is E(Y)?
5. The joint PDF of X and Y is given by s 3 fxy(x, y) = 3 o 0<x<3, 1<y<2, otherwise. Determine P[X<Y]. (8 pts)
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.
6. Suppose X and Y have the joint pdf fr,y) = 2 exp(-:- 0 ) 0< <y otherwise o a. Find Px.x, the correlation coefficient between X and Y. b. Let U = 2X-1 and V=Y +2. What is pu.v, the correlation coefficient between U and V? c. Repeat (b) if U = -TX and V = Y + In 2. d. Let W = Y - X. Compute Var (W). e. Refer to (d). Find an interval that will...
7. The joint pdf of two random variables X and Y is given by 0sxs3,0s y<5 fx(x,y) 15' 0, otherwise Find Cov(X,y)