Let X1, . . . , Xn be i.i.d. uniform on [0, θ].
a. Find the method of moments estimate of θ and its mean and variance.
b. Find the mle of θ.
c. Find the probability density of the mle, and calculate its mean and variance. Compare the variance, the bias, and the mean squared error to those of the method of moments estimate.
d. Find a modification of the mle that renders it unbiased.
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