Geometric distribution is a discrete probability distribution. One definition is that the probability of success for the first time is only obtained in N Bernoulli experiments. Specifically, it is the probability that the Bernoulli test fails the nth time-1and succeeds the nth time. Formula: There are two cases: 1. Successful 1 time, Bernoulli experiment n times, the probability distribution is n, and the value range is [1,2, 3, ...]; 2.m = n- 1 failure, the nth success, the probability distribution of m, the range of values is' 0, 1, 2, 3, ...'. The expectation and variance obtained from two different situations are as follows: e (n) = 1/p, var (n E(m) = (1-p)/p, var (m) = (1-p)/p 2. Event A with a probability of P, with X as the number of tests conducted when A first occurs, then the distribution list of X: P (x = k) = p * (1-p) (k-1), k = 1, 2, 3, ... There is such a random distribution list.