Consider a Bernoulli process where at each step or time there is a success, 1, or failure, 0. $N_k$ denotes the number of successes at the $k^{th}$ step. The probability of success is $p$ and the probability of failure is $q$, where $p + q = 1$.
The problem is to find $$E[3N_5^4 + N_8^3 | N_0, N_1, N_2]$$
I don't understand the problem. I thought that past N have no influence on future N.
I know that $E(N_n) = np$ and $E(N_n^2) = n^2p^2 + npq$, but I don't know how to tackle those greater exponentials.
EDIT:
The problem was actually to show that $$E[3N_5^4 + N_8^3 | N_0, N_1, N_2] = E[3N_5^4 + N_8^3 | N_2]$$