The random variable X has the following probability density function: fX(x) = ( xe−x , if x > 0 0, otherwise. (a) Find the moment generating function of X. (b) Using the moment generating function of X, find E[Xn] for all positive integers n. Your final answer should be an expression that depends only on n.

Follows are the solution to the given points:

Step-by-step explanation:

Given value:

For point a:

Moment generating function of X=?

Using formula:

integrating the values by parts:

Therefore, the moment value generating by the function is

In point b:

Using formula:

form point (a):

Differentiating the value with respect of t

when

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