Suppose that X1,.…,X, is a random sample from the Gamma distribution with density f(x; a, B) = r(a) x > 0 and parameters a, ß > 0. Using the fact, without proof, that the expected value and variance of the Gamma distribution are given by a/ß and a/B², respectively, find the method-of-moment estimator of a and ß.

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Suppose that X1,.…,X, is a random sample from the Gamma distribution with
|density
....
f(t; α, β ) =
r(a)*
r >0
and parameters a, B > 0. Using the fact, without proof, that the expected value
and variance of the Gamma distribution are given by a/ß and a/32, respectively,
find the method-of-moment estimator of a and B.
Transcribed Image Text:Suppose that X1,.…,X, is a random sample from the Gamma distribution with |density .... f(t; α, β ) = r(a)* r >0 and parameters a, B > 0. Using the fact, without proof, that the expected value and variance of the Gamma distribution are given by a/ß and a/32, respectively, find the method-of-moment estimator of a and B.
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