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Let X,..., Xn be exponential with mean beta. Find UMVUEs for beta, beta^2, beta^3. (Use the...

Let X,..., Xn be exponential with mean beta. Find UMVUEs for beta, beta^2, beta^3. (Use the version of the exponential distribution with PDF p(x)= 1/beta e^(-x/beta) (x>0), and so Mx(t)=(1-beta(t))^-1.)

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