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?
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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