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6. (7 points) Suppose that the proportion 6 of defective items in a large shipment is unknown, and that the prior distribution of 0 is

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6. (7 points) Suppose that the proportion 6 of defective items in a large shipment is unknown, and that the prior distribution of 0 is a beta distribution with parameters a = 5 and )3 = 12. Suppose that 25 items are selected at random from the shipment and two of these items are found to be defective. If the square error loss function is used. What is the Bayes estimate 6*(f) of 6

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