Originally Posted by

**Pengu** For this question:

Eva catches two kinds of fish - salmon and trout. Assume salmons and trouts come independently at arrival times of Poisson process with rate 1 per hour and 2 per hour.

Given that Eva caught 3 salmons in the first hour, what is the expected number of fishes she could have caught for the first two hours?

the answer is:

$\displaystyle

E(N_2^{(s)} + N_2^{(t)} | N_1^{(s)} = 3) $

$\displaystyle = E(N_2^{(s)} - N_1^{(s)}| N_1^{(s)} = 3) + E(N_1^{(s)}|N_1^{(s)} = 3) + E(N_2^{(t)}) $

$\displaystyle = 1 + 3 + (2)(2) = 8 $

can someone please explain how to get the second line? like is there some sort of formula to get that?