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Maximum Likelihood Estimate & Fisher Information

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A random sample of n observations is taken from a Poisson distribution with menu theta and the probability mass function attached.
a) Write down the likelihood function
b) Use the method of maximum likelihood to find the maximum likelihood estimator for theta. Confirm that you have located a maximum.
c) Find Fisher's information about theta.

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The attachment gives detailed steps on finding the maximum likelihood estimate and fisher information for Poisson distribution.

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