⑤. (a) Find cov(W,Z) for W and Z defined in Problem 1. e loint densitv of...
6. (a) Find cov(W, Z) for W and Z defined in Problem 1. (b) The joint density of random variables X and Y is f(x,y)-10,' elsewhere. Find cov(X, Y).
22 If f(L,y) = 561, for 0 <<<y<1. find o elsewhere, (a) f(y) (b) f(z|y) (c) E[X | Y = y) (d) EX | Y = 0.5]
If two random variables have the joint density (x + y2), for 0 < x < 1, 0 < y < 1 0, elsewhere. find the probability that 0.2 < X < 0.5 and 0.4 <Y < 1.6. With reference to the previous Problem 6, find both marginal densities and use them to find the probabilities that a. X > 0.8; b. Y < 1.5.
Let X and Y be two continuous random variables having the joint probability density 24xy, for 0 < x < 1,0<p<1.0<x+y<1 0, elsewhere Find the joint probability density of Z X + Y and W-2Y.
14. Random variables X and Y have a density function f(x, y). Find the indicated expected value. f(x, y) = (xy + y2) 0<x< 1,0 <y<1 0 Elsewhere {$(wyty E(x2y) = 15. The means, standard deviations, and covariance for random variables X, Y. and Z are given below. LIX = 3. HY = 5. Az = 7 Ox= 1, = 3, oz = 4 cov(X,Y) = 1, cov (X, Z) = 3, and cov (Y,Z) = -3 T = X-2...
Let X, Y E [0, 1] be distributed according to the joint distribution Íxy (z, y) 6xy2 . Let -XY-3 . Find P(Z < 1 /2)
The joint probability density function is f(x, y) for 17. Find the mean of X given Y = random variables X and Y fax, y) = f(xy *** Q<x<10<x<1 Elsewhere w 14. Random variables X and Y have a density function f(x, y). Find the indicated expected value f(x, y) = 6; (xy+y4) 0<x< 1,0<y<1 0 Elsewhere E(x2y) = 15. The means, standard deviations, and covariance for random variables X, Y, and Z are given below. Lex= 3, uy =...
the answer should be 1/2y^2
3. Suppose the joint density of X and Y is defined by if 0<r<y< 1 f(x,y)= elsewhere. What is E (X2Y = ) ?
. Let X and Y be the proportion of two random variables with joint probability density function f(r, y) e-*, 0, if, 0 < y < x < oo, elsewhere. a) Find P(Xc3.y-2). b) Are X and Y independent? Why? c) Find E(Y/X)
t X and Y be independent random variables with variance ơ1 and ơ3. respectively. Consider the sum. Z=aX + (1-a)% 0 < a < 1 Le Find a that minimizes the variance of Z