- #1

Linder88

- 25

- 0

## Homework Statement

Determine ##P(X<Y|x>0)##

## Homework Equations

X and Y are random variables with the joint density function

$$

f_{XY}(x,y)=

\begin{cases}

4|xy|,-y<x<y,0<y<1\\

0,elsewhere

\end{cases}$$

The marginal densities are given by

$$

f_X(x)=2x\\

f_Y(y)=4y^3

$$

## The Attempt at a Solution

The formula for conditional probability is

$$

P(B|A)=\frac{P(B\cap A)}{P(A)}

$$

In this case we have

$$

P(X<Y|x>0)=\frac{P(X<Y\cap x>0)}{P(x>0)}=\frac{F_{XY}(x,y)}{F_X(x)}=\frac{\int_{}4|xy|dxdy}{\int_0^{\infty}2xdx}

$$

This is where I get stuck, I do not know what boundaries I should put for the joint density function, can someone please help me?