Hierarchical modeling to specify the joint distribution

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Reference no: EM131769272

Question: In an accelerated life testing experiment, different batches of n equipment are operated under different stress conditions. Because the stress level is randomly set for each batch, the probability, P, with which an equipment will last more than T time units is a random variable. In this problem it is assumed that P is discrete, taking the values 0.6, 0.8, and 0.9 with corresponding probabilities 0.2, 0.5, and 0.3. Let Y denote the number of equipment from a randomly selected batch that last more than T time units.

(a) Use the principle of hierarchical modeling to specify the joint distribution of (P, Y). (Hint. Given that P = p, Y ∼ Bin(n, p).)

(b) Find the marginal PMF of Y when n = 3.

Reference no: EM131769272

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