Thread: Joint Probability Density Function

The joint probability density function of a random vector (X,Y) is

f(x,y) = 2 for 0<x<1, 0<y<1, 0<x+y<1,
0 otherwise.

Calculate Pr(X>Y).

Find the conditonal density function of X given Y=0.3

Originally Posted by maibs89

The joint probability density function of a random vector (X,Y) is

f(x,y) = 2 for 0<x<1, 0<y<1, 0<x+y<1,
0 otherwise.

Calculate Pr(X>Y).

Find the conditonal density function of X given Y=0.3

1. Integrate the joint pdf over the region bounded by the lines y = x, x + y = 1 and y = 0.

2. Definition: where is the marginal pdf of Y.