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Problem 1: Suppose that 100 items are sampled from a manufacturing process and 3 are found to be defective. A beta prior is used for the unknown proportion of defective items.

Consider two cases: (1) a = b = 1, and (2) a = 0.5 and b = 5. Plot the two posterior distributions and compare them. Find the two posterior means and compare them. Explain the differences.

Fig: 1