Question

Let X1 , X2 , X3 , X4 be a random sample of size 4 from...

Let X1 , X2 , X3 , X4 be a random sample of size 4 from a geometric distribution with p = 1/3.

A) Find the mgf of Y = X1 + X2 + X3 + X4.

B) How is Y distributed?

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Answer #1

Answer:-

Given That:-

Let be a random sample of size 4 from a geometric distribution with p = 1/3

a)Find the mgf of .?

We know that if are the observation of a random sample from the distribution with the moment - generating function  , then the moment - generating function is . Find the moment - generating function of the geometric distribution with p=1/3.

Find the m.g.f of .

b)How is Y distributed.?

The m.g.f of Y indicates Y has a negative binomial distribution with r = 4, p = 1/3.

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