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Problem 4. The number of murders in Gotham on any given week is assumed to be Poisson with unknown mean λ, with different weeks independent. (a) We observe there were 2 murders one week. What is the value of λ for which this is most likely? (b) we observe for a second week, and there is murder. What is the value of λ for which these observations are most likely? (c) Generalize the above to observations a1,... ,ak over k weeks.

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Answer #1

xl 3 2. are there br wee it A,l 齐.

For the generalised part, after differentiating joint distribution lambda comesout to be mean of mean of the observation.

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