Expectation and Variance of Poisson Distribution equal its Parameter

Theorem
Let $X$ be a discrete random variable with the Poisson distribution with parameter $\lambda$.

Then the expectation of $X$ equals the variance of $X$, that is, $\lambda$ itself.

Proof
From Expectation of Poisson Distribution:
 * $E \left({X}\right) = \lambda$

From Variance of Poisson Distribution:
 * $\operatorname {var} \left({X}\right) = \lambda$