Poisson Question Derivation

Question

How is the second last line obtained from the line before it?

Answer 1

$y$ varies from $x$ to $\infty$.

So, let $z= y-x \Rightarrow z$ varies from $0$ to $\infty$

$$\sum_{z=0}^{\infty}\frac{((1-p)\lambda)^z}{z!} = e^{(1-p)\lambda}$$

This is the Sigma notation of $${e^x}=\sum_{k=0}^\infty\frac{x^k}{k!}$$