Suppose that X1, X2, . . . , Xn are i.i.d. random variables on the interval [0, 1] with the density function
where α > 0 is a parameter to be estimated from the sample. It can be shown
a. How could the method of moments be used to estimate α?
b. What equation does the mle of α satisfy?
c. What is the asymptotic variance of the mle?
d. Find a sufficient statistic for α.
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