X and Y have the following joint probability density functio

X and Y have the following joint probability density function f(x, y) = x + y, if 0 < x < 1 and 0 < y < 1;

0, otherwise.

1. Are X and Y independent?

2. Find the density function of X

Solution

f(x,y) = x+y

fx = x+1/2, 0<x<1

fy = y+1/2, 0<y<1

f(x,y) not equals fx *fy

Hence X and y are not independent.

Density X = x+1/2, 0<x<1