The number of patients, x, arriving at a hospitals emergency room in a night has a Poisson
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Question:
The number of patients, x, arriving at a hospital’s emergency room in a night has a Poisson distribution with expected value λ. Over the last three
nights there were 20, 26, 25 patients. A log-uniform prior is assumed for λ.
(a) Find the posterior density for λ.
(b) Write the R-code computing the posterior probability that there are more than 27 patients on average.
(c) How many patients are expected in a night for the next two days given data?
(d) Over the next two nights, total 52 patients came and now five records are available. Update the density for λ given the record of five nights.
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