Let X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p). Determine the variance of the random variable 2X2^X2X.
(1+3p)n−(1+p)2n(1+3p)^n - (1+p)^{2n}(1+3p)n−(1+p)2n
(1+4p)n−(1+2p)n(1+4p)^n - (1+2p)^n(1+4p)n−(1+2p)n
2^{np(1-p)}
n p (1-p) 2^{2n}