Suppose that X1, X2, . . . , Xn are i.i.d. with density function
and f (x|θ) = 0 otherwise.
a. Find the method of moments estimate of θ.
b. Find the mle of θ. (Hint: Be careful, and don’t differentiate before thinking. For what values of θ is the likelihood positive?)
c. Find a sufficient statistic for θ.
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