Question : A Binomial variate has the mean and standard deviation . Find its moment generating function. Hence obtain . Also compute
First you need the value of n and p. Get them by solving the following equations:
Mean: np = 6 .... (1)
Variance: np(1-p) = 2 .... (2)
Substitute the values of p and n into the moment generating function m(t), which is found here: Binomial distribution - Wikipedia, the free encyclopedia
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Hello,
You may also use the probability generating function (only available for discrete distributions), because its second derivative taken at is just