Geometric

Represents the number of Bernoulli trials needed to get the first success.

Create a new Geometric distribution

Geometric X = Geometric(p); 

creates a discrete Geometric probability distribution.

Distribution properties:

Property	Type/Return type	Description
p	double -> [0, 1]	Probability of a successful trial.
E()	double	Returns the expected value of executed Bernoulli trials before a successful trial.
D()	double	Represents variance, that measures the spread of dispersion of the random variable around its expected value E(X).
P(int k)	double	Probability that the first success occurs on the exactly 𝑘-th trial: P(X = k)
P_LT(int k)	double	Probability that the first success occurs on less than 𝑘-th trials: P(X < k)
P_LTE(int k)	double	Probability that the first success occurs on less than or exactly 𝑘-th trials: P(X ≤ k)
P_HT(int k)	double	Probability that the first success occurs on higher than 𝑘-th trials: P(X > k) = P(X ≤ k)
P_HTE(int k)	double	Probability that the first success occurs on higher than or exactly 𝑘-th trials: P(X ≥ k) = P(X < k)

Example

Example of a geometric distribution

//Example: A basketball player has a 20% chance of making a free throw. 
//What's the probability of his first successful free throw on his 4th attempt?
double p = 0.2; //probability of a successful event
Geometric X = Geometric(p);
std::cout << X.P(4) << std::endl; //0.1024

Common errors

Geometric X = Geometric(1.2); // Error: Probability cannot be less than 0 or more than 1.
std::cout << X.P(0) << std::endl; // Error: Number of trials cannot be less than 1. 

Good to know: k cannot be less than 1 and probability p cannot be outside the bounds of [0, 1].