Let N be a poisson random variable with parameter µ, and conditional on N, let M have a binomial distribution with parameters N and p. Then...

Question

https://i.gyazo.com/3f6b7a71c5d32fa7c309a2e959610480.png

Help me understand what happens from line 2 to line 3. What rules are applied?

Answer 1

Easy....

$$p^k(1-p)^{n-k}\mu^n=\underbrace{(\mu p)^k}_{\text{out of the sum}}\cdot[\mu(1-p)]^{n-k}$$