Independent exponential random variables - find the joint probability distribution

Let X and Y be independent exponential random variables with and

Find the joint probability distribution .

I know that the probability density function for X is for x>0 and 0 otherwise.

also

I know that the probability density function for Y is for x>0 and 0 otherwise.

I am not sure about jointly. Do I simply multiply them together?

Find .

I have no idea how to begin this part, although I know the answer is .04.

Can anyone help?

Re: Independent exponential random variables - find the joint probability distributio

Use the following result: if and are two independent random variables which have a density, namely for and for , then has a density , which is given by .

Re: Independent exponential random variables - find the joint probability distributio

Quote:

Originally Posted by

**CountingPenguins** Let X and Y be independent exponential random variables with

and

Find the joint probability distribution

.

I know that the probability density function for X is

for x>0 and 0 otherwise.

also

I know that the probability density function for Y is

for x>0 and 0 otherwise.

I am not sure about jointly. Do I simply multiply them together?

Find

.

I have no idea how to begin this part, although I know the answer is .04.

Can anyone help?

The definition of independence is that

CB

Re: Independent exponential random variables - find the joint probability distributio