For X∼Bernoulli(p)X \sim \text{Bernoulli}(p)X∼Bernoulli(p), what is the MGF MX(t)M_X(t)MX(t)?
p+(1−p)etp + (1-p)e^tp+(1−p)et
pet+1−ppe^t + 1-ppet+1−p
petpe^tpet
1−p+et1-p+e^t1−p+et