Question

Let X1, . . . , Xn be a random sample from a Poisson distribution. (a)...

Let X1, . . . , Xn be a random sample from a Poisson distribution.

(a) Prove that Pn i=1 Xi is a sufficient statistic for λ.

(b) The MLE for λ in a Poisson distribution is X. Use this fact and the result of part (a) to argue that the MLE is also a sufficient statistic for λ.

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Answer #1

a)

b)

hence is MLE of

Xbar = sum Xi /n

since sum Xi is sufficient

so is

hence MLE is also a sufficient statistic for λ.

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