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

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

score 1 · Accepted Answer · answered Oct 30 '20 at 13:13

1

Easy....

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

answered Oct 30 '20 at 13:13

tommik

@SebastianNielsen :?? it's a basic arithmetic property on exponentiation as $2^7=2^3\cdot2^4$. – tommik Oct 30 '20 at 13:24
Yea, you're right – Sebastian Nielsen Oct 30 '20 at 13:26

1 Answers1