Question: 23. Define the moment generating function of a random variable X. If X and Y are independent random variables with moment generating functions MX (t

23. Define the moment generating function of a random variable X.

If X and Y are independent random variables with moment generating functions MX (t ) and MY (t ), respectively, find the moment generating function of X + Y .

For n = 1, 2, . . . , let Xn have probability density function fn(x) =

(n − 1)!

xn−1e−x for x > 0.

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