If $X_i \sim POI(\lambda)$ I need to know what is the sample mean and sample variance of $\overline{X}$

Question

Consider a random sample from a Poisson distribution If $X_i \sim POI(\lambda)$ I need to know what is the sample mean and sample variance of $\overline{X}$

Ok I know that if $X_1, X_2, .. , X_n$ is a random sample of f(x) with $E(X)= \mu$ and $V(X)= \sigma^2$ then $E(\overline{X})= \mu$ and $V(\overline{X})= \sigma^2/n$ but in my case I dont know how is $E(\overline{X})$ and $V(\overline{X})$ where $X_i \sim POI(\lambda)$

Answer 1

$$E[\overline {X}]=\lambda$$

$$V[\overline {X}]=\frac{\lambda}{n}$$

... the proof is trivial

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The random sample's elements are random variables themselves....thus Capital letter is required (question edited)