# Probability Density Function

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• Mar 25th 2009, 07:34 PM
Len
Probability Density Function
Consider the joint cumulative distribution function $\displaystyle H(x,y)$ where

$\displaystyle H(x,y) = F(x)G(y){1+\frac{1}{2}[1-F(x)][1-G(y)]}$

and $\displaystyle F(x)$ and $\displaystyle G(y)$ are both cumulative distribution function of an exponential distribution with a mean value of 1. Determine a joint probability density function of X and Y.

Not sure how to approach or do this. Thanks for the help.
• Mar 27th 2009, 04:19 AM
mr fantastic
Quote:

Originally Posted by Len
Consider the joint cumulative distribution function $\displaystyle H(x,y)$ where

$\displaystyle H(x,y) = F(x)G(y){1+\frac{1}{2}[1-F(x)][1-G(y)]}$

and $\displaystyle F(x)$ and $\displaystyle G(y)$ are both cumulative distribution function of an exponential distribution with a mean value of 1. Determine a joint probability density function of X and Y.

Not sure how to approach or do this. Thanks for the help.

$\displaystyle h(x, y) = \frac{\partial^2 H(x, y)}{\partial x \partial y}$.