Question : A Binomial variate has the mean and standard deviation . Find its moment generating function. Hence obtain . Also compute

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- Dec 14th 2009, 02:39 AMzorroCompute E[X(X-1)]
Question : A Binomial variate has the mean and standard deviation . Find its moment generating function. Hence obtain . Also compute

- Dec 14th 2009, 03:37 AMmr fantastic
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

. - Dec 18th 2009, 08:27 PMzorroThank u Mr fantastic
- Dec 18th 2009, 10:04 PMzorroIs this correct

http://www.mathhelpforum.com/math-he...4a5f9dd5-1.gif. = = 2............Is this correct ? - Dec 19th 2009, 01:16 AMMoo
Hello,

You may also use the probability generating function (only available for discrete distributions), because its second derivative taken at is just