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Suppose that the proportion theta of bad apples in a large lot is unknown, and has the following prior p.d.f.: c(theta) = { 60theta^2(1 - theta)^3 for 0 < theta < 1} and 0 otherwise. Suppose that a random sample of 10 apples is drawn from the lot, and it is found that 3 are bad. Find the Bayes estimate of theta with respect to the squared error loss function.
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    Carlos Rodriguez <carlos@math.albany.edu>
    This problem was contributed by a student. It is offered as it is with no warranty of any kind
    Last modified: Wed May 13 12:29:11 EDT 1998