Question: 1. Let X1, X2, . . . , X be a random sample from a continuous distribution with pdf 0 otherwise where 9 > 1

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1. Let X1, X2, . . . , X\" be a random sample from a continuous distribution with pdf 0 otherwise where 9 > 1 is an unknown parameter of interest. (21) Find the mean of X1. (4 pts) (b) Find the method of moments estimator g for 3. (4 pts) (c) Find the maximum likelihood estimator g for I9. (8 pts) (hint: start by finding the (joint) tog-liketihood for the sample) ((21) The mean oft;i is ESQ) = i9 and its variance is Var() ). Is 63 biased? 111 1 = (n1}2(n2 Determine the mean squared error (MSE) of 3. (5 pts)

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