Exponential distribution has pdf f(x) = de-dr, > 0 for A> 0, and its mgf is given by 1 m(t) = 1–t/X' Consider X1,..., Xn ~ exp(), where X1,..., Xn are all independent of each other. Define Y = Using the mgf method, show that Y ~ I(n, ). %3D

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Exponential distribution has pdf
f(r) = de-A2, >0
for A > 0, and its mgf is given by
1
m(t)
1-t/A
Consider X1,..., Xn
Using the mgf method, show that Y ~ I(n, ).
exp(A), where X1,..., Xn are all independent of each other. Define Y
Transcribed Image Text:Exponential distribution has pdf f(r) = de-A2, >0 for A > 0, and its mgf is given by 1 m(t) 1-t/A Consider X1,..., Xn Using the mgf method, show that Y ~ I(n, ). exp(A), where X1,..., Xn are all independent of each other. Define Y
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From the given information, X follows exponential distribution.

The probability density function of X is

Statistics homework question answer, step 1, image 1

The mgf is

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