Product of two random variables

Hi guys,

Need a hint with the following problem:

Let and be independent random variables, with probability distribution functions and . Let What is the probability distribution function for ?

Since and are independent, this gives:

Thus, we can obtain by differentiating both sides w/ respect to and using the fundamental theorem of calculus, which gives

Thanks any help!

James

Re: Product of two random variables

Quote:

Originally Posted by

**james121515** Hi guys,

Need a hint with the following problem:

Let

and

be independent random variables, with probability distribution functions

and

. Let

What is the probability distribution function for

?

Since

and

are independent, this gives:

Thus, we can obtain

by differentiating both sides w/ respect to

and using the fundamental theorem of calculus, which gives

Thanks any help!

James

http://www.math.wm.edu/~leemis/2003csada.pdf

Product distribution - Wikipedia, the free encyclopedia

Re: Product of two random variables

Hey,

Interesting, you have the same question as I have!

http://www.mathhelpforum.com/math-he...es-192173.html

I'm specifically looking for the case where X is exponentially distributed, and Y follows a normal distribution.

A closed-form solution seems impossible, hence I tried to estimate the pdf of Z.

Via Monte Carlo simulation, it appears that Z=XY, follows again an exponential distribution for z>0.