this is the answer 7. Let X and Y have joint density (x + y) for 0 < 2y 52 51 f(x, y) = ? otherwise. What is the conditional expectation of X given Y =y? We were unable to transcribe this image
Let X and Y be a random variable with joint PDF: f X Y ( x , y ) = { a y x 2 , x ≥ 1 , 0 ≤ y ≤ 1 0 otherwise What is a? What is the conditional PDF of given ? What is the conditional expectation of given ? What is the expected value of ? Let X and Y be a random variable with joint PDF: fxv (, y) = {&, «...
Exercise 6.B.3. Let the pair of random variables (X, Y) have joint density function f(x, y)-16(x-y)2 įf x, y e [0, 11, 0 otherwise. a. Confirm that f is a joint density function by verifying that equation (6.B.4) holds, and use a computer or graphing calculator to sketch its graph. b. Compute the marginal density function of Y c. For each x e [0,1], compute the conditional density of Y given x. d. Compute the conditional expectation function E(Y|X =...
the answer should be 4/3 x u Lipulation of X given Y =y? 10. Let X and Y have joint density (2xy for 0 Sy < 2x < 2 f(x, y) = { otherwise. What is the conditional expectation of Y given X = r?
2.8.14 Let X and Y have joint density fX,Y (x, y) = (x2 + y)/36 for −2 < x < 1 and 0 < y < 4, otherwise fX,Y (x, y) = 0. (a) Compute the conditional density fY|X (y|x) for all x, y ∈ R1 with fX (x) > 0. (b) Compute the conditional density fX|Y (x|y) for all x, y ∈ R1 with fY (y) > 0. (c) Are X and Y independent? Why or why not?
3. Let the random variables X and Y have the joint probability density function 0 y 1, 0 x < y fxy(x, y)y otherwise (a) Compute the joint expectation E(XY) (b) Compute the marginal expectations E(X) and E (Y) (c) Compute the covariance Cov(X, Y)
Let X and Y be a random variable with joint PDF: fxx (x, y) = { 1, 2 > 1,0 Sysi 0 otherwise 1. What is a? 2. What is the conditional PDF fy|x(x|y) of Y given X = x? 3. What is the conditional expectation of Ygiven X? 4. What is the expected value of Y?
3. Let the random variables X and Y have the joint probability density function fxr (x, y) = 0 <y<1, 0<xsy otherwise (a) Compute the joint expectation E(XY). (b) Compute the marginal expectations E(X) and E(Y). (c) Compute the covariance Cov(X,Y).
Let the random variable X and Y have the joint probability density function. fxy(x,y) lo, 3. Let the random variables X and Y have the joint probability density function fxy(x, y) = 0<y<1, 0<x<y otherwise (a) Compute the joint expectation E(XY). (b) Compute the marginal expectations E(X) and E(Y). (c) Compute the covariance Cov(X,Y).
. (Dobrow, 1.13) Random variables X and Y have joint density fX,Y = ( 3y 0 < x < y < 1 0 otherwise (a) Find the conditional density of Y given X = x. (b) Compute E[Y | X = x]. (c) Find the conditional density of X given Y = y. Describe the conditional distribution. I. (Dobrow, 1.13) Random variables X and Y have joint density 0 otherwise (a) Find the conditional density of Y given X (b)...