Let \(Y\) be the number of counts of a Poisson random variable with mean . Suppose the 5 possible values of are \(1,2,3,4\), and 5 . We do not have any reason to give any possible value more weight than any other value, so we give them equal prior weight. \(Y=2\) was observed. Find the posterior distribution by filling in the simplified table.

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prior likelihood prior likelihood posterior marginal P(Y = 2