(Maximum likelihood estimation) Suppose that X, ..., Xn are independently sampled from a Pareto distribution with...

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(Maximum likelihood estimation) Suppose that X₁, ..., Xn are independently sampled from a Pareto distribution with the pdf a -= {o= 0 f(x; α, 3) = xa+1 x ≥B, x < B, where a, ß> 0. (a) (15 points) Suppose ß is known. Find the maximum likelihood estimator of a. (b) (15 points) Suppose a is known. Find the maximum likelihood estimator of ß. (Maximum likelihood estimation) Suppose that X₁, ..., Xn are independently sampled from a Pareto distribution with the pdf a -= {o= 0 f(x; α, 3) = xa+1 x ≥B, x < B, where a, ß> 0. (a) (15 points) Suppose ß is known. Find the maximum likelihood estimator of a. (b) (15 points) Suppose a is known. Find the maximum likelihood estimator of ß.