Question: Assume is a Pareto random variable with PDF given by () = (+1) , 1 where is positive number between 0 and 1, i.e., (0,1).

Assume is a Pareto random variable with PDF given by () = (+1) , 1 where is positive number between 0 and 1, i.e., (0,1).

a) Show that = ln() is has exponential distribution, exp().

b) Find the maximum likelihood estimator of . And explain why moment of method fails to work in this case.

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