Question

how can I know if my problem is of the geometric distribution problem?

Answer 1

In probability theory and statistics, the geometric distribution is either of two discrete probability distributions:

• The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ...}
• The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... }

Geometric Distributions

Instead of counting the number of successes, we can also count the number of trials until a success is obtained. That is, we shall let the random variable X represent the number of trials needed to obtain the first success. In this situation, the number of trials will not be fixed. But if the trials are still independent, only two outcomes are available for each trial, and the probability of a success is still constant, then the random variable will have a geometric distribution.

P(X = k) = (1-p)^(k-1) p