Question: Take the exponential density f (x j ) 1 exp x for 0. (a) Find the conjugate prior

Take the exponential density f (x j ¸) Æ 1

¸ exp

¡

¡x

¸

¢

for ¸ È 0.

(a) Find the conjugate prior ¼(¸).

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

(c) Find the posterior meanb¸

Bayes.

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