If X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p), what is the moment generating function MX(t)M_X(t)MX(t)?
(p+(1−p)et)n(p + (1-p)e^t)^n(p+(1−p)et)n
((1−p)+pet)n((1-p) + pe^t)^n((1−p)+pet)n
enp(et−1)e^{np(e^t-1)}enp(et−1)
pnentp^n e^{nt}pnent