Question: 1. Find the Maximum Likelihood Estimator for a random sample X1, . . . , Xn from the distribution f(x, ) =(1/2 3 )x 2

1. Find the Maximum Likelihood Estimator for a random sample X1, . . . , Xn from the distribution f(x, ) =(1/2³)x²e^-x/ with 0 < x < , 0 < < .

2. Suppose X1, . . . , Xn is a random sample from a distribution with a pdf f(x, ) = (1 x)¹ for 0 < x < 1 and0 < . Find the best critical region for testing H0 : = 1 versus H1 : = 5.

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