Let the random variables X and Y have the following joint probability density function.
f (x, y) = 6(y − x), 0 < x < y < 1 If the marginal distributions are:
f(x) = 3(x − 1)2, 0 < x < 1f(y) = 3y2, 0 < y < 1
Find the correlation of X and Y .
Let the random variables X and Y have the following joint probability density function. f (x,...
The continuous random variables, X and Y , have the following joint probability density function: f(x,y) = 1/6(y2 + x3), −1 ≤ x ≤ 1, −2 ≤ y ≤ 1, and zero otherwise. (a) Find the marginal distributions of X and Y. (b) Find the marginal means and variances. (c) Find the correlation of X and Y. (d) Are the two variables independent? Justify.
Let X and Y be random variables with joint probability density function f(x, y) = {Cxe for 0 SXS 4,0 s y soo otherwise. Find the marginal probability density function fx(x).
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)
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 X and Y be two random variables with the joint probability density function: f(x,y) = cxy, for 0 < x < 3 and 0 < y < x a) Determine the value of the constant c such that the expression above is valid. b) Find the marginal density functions for X and Y. c) Are X and Y independent random variables? d) Find E[X].
Problem 1. Let X and Y be continuous random variables with joint probability density function f(x,y) distributions for X and Y are (i/3) (x +y), for (x, y) in the rectangular region 0ss1,0Sys 2. The two marginal Ix(x)- (z+1), if 0 251 fy(y) = (1+2y), if0 y 2 Calculate E(x IY -v) and Var (X |Y ) for each y l0,2).
em 1. Let X and Y be continuous random variables with joint probability density function y S 2. The two marginal Probl f(z, y) = (1/3)(z + y), fr (zw) in the rectangular region 0 distributions for X and Y are z 1,0 Calculate E(XIY_y) and Var (지Y-y) for each ye[O,2].
stats (6) Consider the following joint probability density function of the random variables X and f(x,y) = 9, 1<x<3, 1<y< 2, elsewhere. (a) Find the marginal density functions of X and Y. (b) Are X and Y independent? (c) Find P(X > 2).
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...