# Math Help - Exponential random variable

1. ## Exponential random variable

Hi members,
Show that
$E[X^4]=[24]/[\lambda^4]$
When X is an exponential random variable with rate $\lambda$

2. ## Re: Exponential random variable

You can do this using the moment generating function.

$M(t)=E[e^{t X}]$

$E[X^4]=\dfrac {d^4M(t)}{{dt^4}}|_{t=0}$

I leave the details to you.

3. ## Re: Exponential random variable

Or you can use the basic definition: $E(X^4)= \int x^4 P(x)dx$ where P(x) is the probability density.