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# Combined likelihoods for random samples watch

1. How would I go about doing this question?
2. (Original post by Bruce Harrisface)
How would I go about doing this question?
Let's get you started. You are given that the observations are independent of one another - therefore to get the combined likelihood, you simply multiply together the likelihoods for each individual observation. They are all Poisson distributed, so we can simply write down the Poisson likelihood for the x's and the y's.

and

Now multiply these together for all the and , and you have the combined likelihood as a function of

The second part of the question simply requires you to (a) set in this expression and then differentiate w.r.t. to get the maximum likelihood estimate. (b) is similar, but messier. Can you now do (c) yourself?

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