Question

In: Statistics and Probability

1) Suppose X1,X2,...,Xn are iid Gamma(α,λ) random variables. a) Express the first and third moments (µ1...

1) Suppose X1,X2,...,Xn are iid Gamma(α,λ) random variables.

a) Express the first and third moments (µ1 = E(X) and µ3 = E(X3)) as functions of λ and α.

b) Solve this system of equations to find estimators of ˆ λ and ˆ α as functions of the empirical moments. Note that the estimates must be positive.

2) Suppose that X1,X2,...,Xn are a iid Beta(a, a) random variables. That is, a beta distribution with the restriction that b = a. Using the formulae for the expectation and/or variance, find a method of moments estimator for a.

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