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What are the pdf, the mean, and the variance of X if the moment-generating function of X
Chapter 3, Problem 3.2-1(choose chapter or problem)
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.
Questions & Answers
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.