# Statistics – Method of estimating moments of a Poisson (\$ theta \$)

Leave $$X_1, ldots, X_n$$ ~ Poi ($$theta$$). Calculate the moments estimators for. $$theta$$ in the following cases:
Remember it $$E (X_1) = Var (X_1) = theta$$

(a) $$hat { theta} _1$$ Equating the first non-central theoretical moment with the first non-central empirical moment.

(second) $$hat { theta} _2$$ equaling the theoretical variance with the empirical variance.

(do) $$hat { theta} _3$$ Equating the second non-central theoretical moment with the second non-central empirical moment.

I just want to know if I did it correctly. It seems too easy.

(a) $$hat { theta} _1 = overline {x} = frac {1} {n} sum ^ {n} _ {i = 1} x_i$$

(second) $$hat { theta} _2 = line {x} = frac {1} {n} sum ^ {n} _ {i = 1} (x_i- mu_1) ^ 2$$

(do) $$hat { theta} _3 ^ 2- hat { theta} _3 = frac {1} {n} sum ^ {n} _ {i = 1} x_i ^ 2$$