Problem B. Let X and Y have joint density Show that Y and X/Y are independent.
9 Let X and Y have the joint probability density function f(x, y) ={4x for 。< otherwise a) What is the marginal density function of Y, where nonzero? b)Are X and Y stochastically independent 9 Let X and Y have the joint probability density function f(x, y) ={4x for 。
Let X and Y have joint density f(x, y) = e−y 1[0 < x < y] Show that Y and X/Y are independent.
Let X and Y have joint density function: show s c(x² + y²), if os rs1.osys1 10, otherwise. (a) Determine the constant c. (b) Find P(X < 1/2, Y > 1/2), and P(Y < 1/2). (c) Find P(X - Y < 1/2) (d) Find the covariance Cov(X,Y). Are the random variables X and Y independent? (e) Find the correlation coefficient p.
(1 point) Let X and Y have the joint density function (a) What is the joint density function of U,V? (b) On what domain is this defined? and (1 point) Let X and Y have the joint density function (a) What is the joint density function of U,V? (b) On what domain is this defined? and
(a) Show that fY X(y; x) is a valid density function. (b) Find the marginal density of Y as a functon of the CDF (c) Find the marginal density of X. (d) Deduce P[X < 0:2]. (e) Are Y and X independent? Problem 2: Suppose (Y, X) is continuously distributed with joint density function (a) Show that fyx(y, x) is a valid density function (b) Find the marginal density of Y as a functon of the CDF Φ(t)-let φ(z)dz. (c)...
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?
Let X and Y have joint density xY)0otherwise. 0 otherwise (a) Find k. (b) Compute the marginal densities of X and of Y (c) Compute P(Y 2x). (d) Compute P(X-Y| 〈 0.5). (e) Are X and Y independent?
Show that random variables X and Y are not independent if the joint density function is given as fxx(x, y) = u(x)uy)xe-x(y+1)
Let X and Y have joint density Jxy(Cr,9)0otherwise. (a) Compute the marginal densities of X and Y. (b) Compute P(y 〉 2X). (c) Are X and Y independent?
Problem 8: Let X and Y be continuous random variables. The joint density of X and Y is given by: fxy (x, y)2 if 0 yx< 1. Find the correlation coefficient of X and Y, pxy. Problem 8: Let X and Y be continuous random variables. The joint density of X and Y is given by: fxy (x, y)2 if 0 yx