Consider the independent observations x1, x2, . . . , xn from the gamma distribution with...

Consider the independent observations x1, x2, . . . , xn from the gamma distribution with pdf f(x) = (1/ Γ(α)β^α)x^(α−1)e ^(−x/β), x > 0 and 0 otherwise.

a. Write out the likelihood function

b. Write out a set of equations that give the maximum likelihood estimators of α and β.

c. Assuming α is known, find the likelihood estimator Bˆ of β.

d. Find the expected value and variance of Bˆ

Expert Solution

orchestra answered 2 years ago

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