Suppose that X1, X2, . . . , Xn are i.i.d. random variables on the interval [0, 1] with...

Suppose that X₁, X₂, . . . , X_n 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.