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Moment generating function for discrete probability mass function?
Given the discrete r.v. X
with the Probability Mass Function
P(X=x) = 2 (1/3)^x
Find its Moment Generating Function.
Update:
x = 1,2,3,...
Update 2:
I think your answer is wrong since from what I know MGF is E(e^tx) .
2 Answers
Relevance
- cidyahLv 71 decade ago
MGF = E(t^x)
= 2 Σ t^x(1/3)^x
=2 Σ (t/3)^x , x=1,2,.....
Σ (t/3)^x is a geometric series with common ratio t/3 and has the sum:
(t/3) / [1-t/3]
= t /(3-t)
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