What are the pdf, the mean, and the variance of X if the moment-generating function of X

Chapter 3, Problem 3.2-1

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QUESTION:

What are the pdf, the mean, and the variance of X if the moment-generating function of X is given by the following? (a) M(t) = 1 1 3t , t < 1/3. (b) M(t) = 3 3 t , t < 3.

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QUESTION:

What are the pdf, the mean, and the variance of X if the moment-generating function of X is given by the following? (a) M(t) = 1 1 3t , t < 1/3. (b) M(t) = 3 3 t , t < 3.

ANSWER:

Step 1 of 6

(a)

The moment generating function of X is given by:

The moment generating function of exponential distribution with parameter  is:

So, X has the same mgf of exponential distribution with as 3.

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