Find the distributions of the random variables that have each of the following moment generating functions: m(t)=(e^t)/(2-e^t)

nuseldW4r

nuseldW4r

Answered question

2022-11-25

Find the distributions of the random variables that have each of the following moment generating functions:
m ( t ) = e t 2 e t

Answer & Explanation

Aleah Rowe

Aleah Rowe

Beginner2022-11-26Added 15 answers

Moment-generating function for a geometric distribution Y:
m ( t ) = p e t 1 q e t
Rewriting the given function gives:
m ( t ) = e t 2 e t = 1 2 e t 1 1 2 e t
The given equation is of this form with:
p = 1 2 = 0.5
q = 1 2 = 0.5
Result:
Geometric with p=0.5

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