Geometric Distribution:
Consider a sequence of Bernoulli trials (failure and success), the geometric distribution is used to find the number of failures before the first success. For a geometric distribution with probability of success, the probability that exactly x failures occur before the first success is
P(X=x) =
The geometric distribution is the only discrete distribution with the memory less property. The successive probabilities in this distribution form a geometric series, hence the name to the distribution.
- In baseball, a geometric distribution is useful in analyzing the probability of a batter earning a hit before three strikes, a success within 3 trials.
- In cost-benefit analyses, whether to fund research trials that, if successful, will earn the company some estimated profit, getting a success before the cost outweighs the potential gain.
The probability mass function, the probability that the xth trial (out of x trials) is the first success is
f(x) = P(X= x)
MEAN, μ = E(X) =
Variance, 
In Excel, we use the function NEGBINOMDIST(number_f, number_s, probability_s) where
Number_f – number of failures , Number_s – the threshold number of successes(for geometric distribution,1) , Probability_s – the probability of a success on each trial.
Example:
A die is rolled until a 1 shows up. Using the function, resulting geometric distribution is shown graphically
