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Question 1 (a) Determine Var(X) if X~Bin(n,p). (b) Determine Var(X) if X~Poi(λ). Question 2 (a) Show...

Question 1

(a) Determine Var(X) if X~Bin(n,p).

(b) Determine Var(X) if X~Poi(λ).

Question 2

(a) Show that the m.l.e of λ is the sample mean if the data is distributed according to Poi(λ).

(b) Determine the m.l.e of σ if data is independently identically distributed normally.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

In case of binomial and poisson for obtaining variance we have to first obtain the first and second central moment.

For obtaining the mle, we have to maximize the likelihood function. Poisson is one parameter problem so the mle can be obtain simply but in case of normal having two parameter mle can be obtain in two cases with first as a mean know and second mean unknown.

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