Please help me solve questions below. Please give me crystal clear solutions. I would like to see how to solve these problems a,b.. Solution The method of moments estimator of λ = E(x) E(x) = Σ x e^-λ λ^x / x!, x varies from 0 to infinity = λ Σ e^-λ λ^(x-1) / (x-1)!, x from 1 to infinity = λ The first sample moment is xbar , the sample mean Equating the sample and population means, the moment estimate of λ is xbar (the sample mean).

1. Please help me solve questions below. Please give me crystal clear solutions.
I would like to see how to solve these problems a,b..
Solution
The method of moments estimator of λ = E(x)
E(x) = Σ x e^-λ λ^x / x!, x varies from 0 to infinity
= λ Σ e^-λ λ^(x-1) / (x-1)!, x from 1 to infinity
= λ
The first sample moment is xbar , the sample mean
Equating the sample and population means, the moment estimate of λ is xbar (the sample
mean)