# Thread: exponential random variable with a random mean?

1. ## exponential random variable with a random mean?

Hi all,
I'm wondering how could I model a r.v. $B$ which is exponentially distributed (i.e. with pdf $f(b)=kexp(-kb)u(b)$ with $u(b)$ = the step function) but whose parameter $k$ is itself a random variable, not a fixed deterministic value.

Since:
$f(b|k)=f(b,k)/f(k)$
I think I can write:
$f(b,k)=f(b|k)f(k)=kexp(-kb)u(b)f(k)$
is this correct?

Thanks!

2. Hello,

You don't know whether k has a pdf or not. So it's not really correct to write f(k). If you assume so, it's ok.
And your whole formula is ok (actually, u(b)=1 iff b>0)

3. Hi,
I assume that k is a r.v. so as you say everything is ok.

Thanks for confirming it!