1. ## exponential distribution

the random variable X has an exponential distribution with parameter λ = 1. It can be shown that for any nonnegative integer k that: E[X^k]=k!

I am having problems with finding the answer to the problem E[5X^4-18] .

I would liek to know where to begin this problem. Any help would be great.

2. Hello,

By linearity of the expectation, we have :
$E[5X^4-18]=E[5X^4]-E[18]=5E[X^4]-18$