Consider a succession of Bernoulli trials with a success probability of p

Consider a succession of Bernoulli trials with a success probability of p. The probability that the first success occurs after k trials is given by the geometric distribution

P  First success after k trial= Geo.

(The geometric distribution is sometimes defined to be the probability of success after k failures so is defined as p (1 − p) k where k = 0, 1, 2, ...) Compute the CGF for the geometric distribution and from this compute the mean and variance. If the probability of winning a lottery is how many attempts do you have to make on average before you win.