Question: Suppose that the parts produced by a machine can have three different levels of functionality: working, impaired, defective. Let p1, p2, and p3 = 1

Suppose that the parts produced by a machine can have three different levels of functionality: working, impaired, defective. Let p1, p2, and p3 = 1ˆ’ p1 ˆ’ p2 be the probabilities that a part is working, impaired, and defective, respectively. Suppose that the vector p = (p1, p2) is unknown but has a joint distribution with p.d.f.

Suppose that we observe 10 parts that are conditionally independent given p, and among those 10 parts, eight are working and two are impaired. Find the conditional p.d.f. of p given the observed parts. You might find Eq. (5.8.2) helpful.

12 for 0 < Pi, P2 < 1 P2

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