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 $\mathbb{P}[Y \leq X]$.
  • $\begingroup$ What is it you don't understand about the problem? $\endgroup$ – Math1000 Dec 8 '14 at 20:07

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

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


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