1. A geometric random variable X is a discrete variable taking values in {1, 2, ...} with the parameter p which models the probability of getting the first success on the th trial. This variable has...

Extracted text: 1. A geometric random variable X is a discrete variable taking values in {1, 2, ...} with the parameter p which models the probability of getting the first success on the th trial. This variable has density function fx (x) = p(1 – p)®-1. Find the moment generating function of X and use it to find the mean and variance of X.