Let denote the average number of defects per 100 feet of a certain type of magnetic tape Suppose that the value of is unknown and that the prior distribution of is the gamma distribution with parameters 2 and 10 When a 1200 foot roll of this tape is inspected, exactly four defects are found Determine the posterior distribution of

Question: Let denote the average number of defects per 100 feet of a certain type of magnetic tape. Suppose that the value of is

Let θ denote the average number of defects per 100 feet of a certain type of magnetic tape. Suppose that the value of θ is unknown and that the prior distribution of θ is the gamma distribution with parameters α = 2 and β = 10. When a 1200-foot roll of this tape is inspected, exactly four defects are found. Determine the posterior distribution of θ.

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