Each of two classes, A and B, has the same number of risks. In class A, the number of claims per risk per year has mean 1/6 and variance 5/36, while the amount of a single claim has mean 4 and variance 20. In class B, the number of claims per risk per year has mean 5/6 and variance 5/36, while the amount of a single claim has mean 2 and variance 5. A risk is selected at random from one of the two classes and is observed for four years. Suppose the pure premium (frequency times severity) calculated from the four observations is 0.25. Determine the Bühlmann credibility estimate for the risk's pure premium.
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