Take the Pareto density f (x j ) x1 for x 1 and

Question:

Take the Pareto density f (x j ®) Æ

®

x®Å1 for x È 1 and ® È 0.

(a) Find the conjugate prior ¼(®). (This may be tricky.)

(b) Find the posterior ¼(® j X) given a random sample.

(c) Find the posterior mean b®

Bayes.

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