Use the moment-generating function (mgf) of X to find the distribution

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Practice Problems

Question 2

Let X1,X2,..., Xn be iid observations from Bernoulli(p)distribution, the pdf of X is given by

a) Use the moment-generating function (mgf) of X to find the distribution of

(hint: you may use the mgf given in the appendix table)

b) Show that T is sufficient and complete for p (show the steps to get full credicts).

c) Find the UMVUE of p.

Hint

A probability distribution is distinctively established by its MGF. Two random variables have the same MGF if they have a similar distribution. Therefore, the MGF determines the distribution. MGF of x will give out all moments of x thus why it is known as moment generating function....

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