# random variables (X,Y) have the following joint PDF

Let the random variable $(X,Y)$ have the following joint PDF

$$f(x,y) = \left\{ \begin{matrix} 2x^{-(2x+y)}, & x>0, y>0\\ 0, & \text{otherwise} \end{matrix}\right\|.$$

Please find

1. the joint cumulative distribution function (joint CDF) $F(x, y)$ and
2. the probability $\mathbb{P}[Y \leq X]$.
• What is it you don't understand about the problem? – Math1000 Dec 8 '14 at 20:07

## 1 Answer

Hints $$F(x,y) = \mathbb{P}[X \leq x, Y \leq y] = \int_{-\infty}^x \int_{-\infty}^y f(x,y) dxdy$$

and $$\mathbb{P}[Y \leq X] = \iint_{y \leq x} f(x,y) dxdy$$