Suppose X, Y are random variables whose joint PDF is given by fxy(x,y) = { 0<y<1,0<=<y...
Suppose X, Y are random variables whose joint PDF is given by fxy(x, y) 9 { 0 <y <1,0 < x <y y otherwise 0, 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y).
Suppose X, Y are random variables whose joint PDF is given by . 1 0 < y < 1,0 < x < y y otherwise 0, 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate 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. Two random variables X and Y have the following joint probability density function (PDF) Skx 0<x<y<1, fxy(x, y) = 10 otherwise. (a) [2 points) Determine the constant k. (b) (4 points) Find the marginal PDFs fx(2) and fy(y). Are X and Y independent? (c) [4 points) Find the expected values E[X] and EY). (d) [6 points) Find the variances Var[X] and Var[Y]. (e) [4 points) What is the covariance between X and Y?
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).
5. Suppose that the joint pdf of the random variables X and Y is given by - { ° 0 1, 0< y < 1 f (x, y) 0 elsewhere a) Find the marginal pdf of X Include the support b) Are X and Y independent? Explain c) Find P(XY < 1)
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)
Let X and Y be random variables with joint PDF fx,y(x, y) = 2 for 0 < y < x < 1. Find Var(Y|X).
Let the random variables x and y have joint pdf as follows: 4 x < 1,0< y< 3 0 3 2) (round off to third decimal place). Find P(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)?