1. Let X1,..., X, be an iid sample from Bernoulli(p). (a) Find the method of moment estimator of p. (b) Find the MLE for p.
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- Assume X_1, X_2, .....X_n are random samples from X~Exponential(θ).1) Find the MLE estimator of θ .Let X1, . . . , Xn be an iid sample from f(x | θ) = θxθ−1 , 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ.If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameter
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