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1. Remember that a Poisson Distribution has a density function of f(x) = [e^(−k)k^x]/x! . It...

1. Remember that a Poisson Distribution has a density function of f(x) = [e^(−k)k^x]/x! . It has a mean and variance both equal to k.

(a) Use the method of moments to find an estimator for k.

(b) Use the maximum likelihood method to find an estimator for k.

(c) Show that the estimator you got from the first part is an unbiased estimator for k.

(d) (5 points) Find an expression for the variance of the estimator you have found. (e)

(3 points) If we obtained a random sample from a Poisson distribution of 4, 8, 6, 4, 4, 5, 5, 3, what would you estimate k to be?

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