Math Help - Joint Probability Density Function

1. 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

2. 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: $f(x | y) = \frac{f(x, y)}{g(y)}$ where $g(y)$ is the marginal pdf of Y.