# Thread: Proving expected value of Poisson Distribution

1. ## Proving expected value of Poisson Distribution

How can i prove that the expected value of a poisson distribution is lambda?

From the definition: $E(X) = \sum_{x=0}^{+\infty} x \cdot \frac{e^{-\lambda} \lambda^x}{x!} = \lambda e^{-\lambda} \sum_{x=1}^{+\infty}\frac{\lambda^{x-1}}{(x-1)!} = \lambda e^{-\lambda} \sum_{t=0}^{+\infty}\frac{\lambda^{t}}{t!}$ (the missing steps are left for you to fill in) and you should recognise what the sum is equal to ....