Let X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p). What is the expected value of the random variable etXe^{tX}etX?
(pet+1−p)n(pe^t + 1 - p)^n(pet+1−p)n
(p+(1−p)et)n(p + (1-p)e^t)^n(p+(1−p)et)n
e^{n p (e^t - 1)}
n(pe^t + 1 - p)