If XXX is a Bernoulli random variable with P(X=1)=pP(X=1) = pP(X=1)=p, what is the MGF MX(t)M_X(t)MX(t)?
(1−p)+pet(1-p) + pe^t(1−p)+pet
p+(1−p)etp + (1-p)e^tp+(1−p)et
petpe^tpet
epte^{pt}ept