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Let X1, X2,..., Xn be a random sample from a population with probability density function f(x)...

Let X1, X2,..., Xn be a random sample from a population with probability density function f(x) = theta(1-x)^(theta-1), where 0<x<1, where theta is a positive unknown parameter

a) Find the method of moments estimator of theta

b) Find the maximum likelihood estimator of theta

c) Show that the log likelihood function is maximized at theta(hat)

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