① Moment estimation. ∵P(X=k)=[e^(-λ)](λ^k)/(k！ ), k=0, 1, 2, … sample mean X'=( 1/n)∑xi. However, the population mean e (x) = ∑ (xi) p (xi = k) = ∑ k [e (-λ)] (λ k)/(k! )=[e^(-λ)]λ∑(λ^k)/(k！ )=λ。

In addition, the moment estimation of X'=E(X), ∴ λ'=( 1/n)∑xi, i= 1, 2 ..., n.

② Maximum likelihood estimation. Let the likelihood function l (x, λ) = ∏ p (xi = k) = [e (-nλ)] (λ ∑ xi)/∏ [(xi)! ]。 Ask again? [lnL(x，λ)]/？ λ, and let its value be 0, ∴-n+( 1/λ)∑xi=0. Maximum likelihood estimation λ'=( 1/n)∑xi, i= 1, 2, ..., n.

For reference.