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Suppose that the number of defects on a roll of magnetic recording tape has a Poisson...

Suppose that the number of defects on a roll of magnetic recording tape has a Poisson distribution for which the mean λ is known to be either 1 or 5. Suppose the prior pmf for λ is: P[λ = 1] = 0.4 P[λ = 5] = 0.6 Suppose that we examine five tapes, and find that the number of defects are x1 = 3,x2 = 1,x3 = 4,x4 = 6 and x5 = 2. Show that the posterior distribution for λ is: P[λ = 1|¯ x] = 0.012 P[λ = 5|¯ x] = 0.988

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