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.6. The table below shows some data on the number of cases of foodbourne botulism in England and Wales.constant rate A in time and so can be modeled as a random sample from a Poisson distribution with mean X.is believed that cases occur at a

(a) An expert in the epidemiology of similar diseases suggests E(^) :Var(A) = 2. Determine the conjugate prior distribution for A, spec-ifying fully the parameters in this distribution. (b) Derive the posterior distribution for A. (c) As an alternative to the conjugate prior you derived in part (a), the-expert suggests using A~ N(2,2). Would this prior be appropriate-here? Explain your answer.

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