1. ## Joint Probability Function

Hi, Can anyone help? I'm not even sure where to begin with this.

The joint probability density function f(x,y) takes the value 1 inside the triangle T with the vertices (-1,0) (1,0) and (0,1) and f takes value 0 outside the triangle. Find the probability P(X greater or equal Y)

I got as far as drawing a sketch of the triangle.

2. Originally Posted by s7b
Hi, Can anyone help? I'm not even sure where to begin with this.

The joint probability density function f(x,y) takes the value 1 inside the triangle T with the vertices (-1,0) (1,0) and (0,1) and f takes value 0 outside the triangle. Find the probability P(X greater or equal Y)

I got as far as drawing a sketch of the triangle.
The line passing through (-1, 0) and (0, 1) has equation y = x + 1.
The line passing through (1, 0) and (0, 1) has equation y = -x + 1.

$\displaystyle \Pr(X \geq Y) = \int_{y = 0}^{y = 1/2} \int_{x = y}^{x = 1 - y} 1 \, dx \, dy$.

Note: The intersection point of y = x and y = -x + 1 is (1/2, 1/2).