What is the moment generating function from a density of a continuous

[karthik666]

Hi everyone,

So I am taking a statistics course and finding this concept kinda challenging. wondering if someone can help me with the following problem!

Let X be a random variable with probability density function $$f(x)=\begin{cases}xe^{-x} \quad \text{if } x>0\\0 \quad \text{ } Otherwise.\end{cases} $$
we want to Determine the mgf of X whenever it exists.

I know that M(t) = E(e^(tx)) = integral of e^(tx)* f(x)
but not sure what to do from there.

Thanks for the help ^^

 

[MathematicalPhysicist]

It's the integral of e^{tx}*f(x) over $\mathbb{R}$.

 

[karthik666]

what is the approach for this problem?

 

[Office_Shredder]

You should write down explicitly the integral you said you're evaluating, and then try to evaluate it. Why don't you show us what you can do with it and then we can help you with where you get stuck? We can't help you until you do that.