Hypergeometric

Describes the probability of 𝑘 k successes in 𝑛 n draws from a finite population of size 𝑁 N containing exactly 𝐾 K successes, without replacement. It is used when the sample is drawn from a population without replacement, making the trials dependent on each other.

Create a new Hypergeometric distribution

Hypergeometric X = Hypergeometric(K, N, n); 

creates a discrete Hypergeometric probability distribution.

Distribution properties:

Property	Type/Return type	Description
K	int	Successes in population.
N	int	Population size.
n	int	Sample size.
E()	double	Returns the expected value of success items from a sample size n, from a population size N.
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 of getting exactly 𝑘 successes in 𝑛 draws from a population of size 𝑁 with 𝐾 successes: P(X = k)
P_LT(int k)	double	Probability of getting less than 𝑘 successes in 𝑛 draws from a population of size 𝑁 with 𝐾 successes: P(X < k)
P_LTE(int k)	double	Probability of getting less than or exactly 𝑘 successes in 𝑛 draws from a population of size 𝑁 with 𝐾 successes: P(X ≤ k)
P_HT(int k)	double	Probability of getting more than 𝑘 successes in 𝑛 draws from a population of size 𝑁 with 𝐾 successes: P(X > k) = P(X ≤ k)
P_HTE(int k)	double	Probability of getting more than or exactly 𝑘 successes in 𝑛 draws from a population of size 𝑁 with 𝐾 successes: P(X ≥ k) = P(X < k)

Example

Example of a hypergeometric distribution

//Example: Suppose you have a jar containing 15 marbles: 10 red marbles 
//(successes) and 5 blue marbles (failures). You draw 5 marbles without 
//replacement and want to find the probability of drawing exactly 3 red marbles
int K = 10; //4 successful items (red marbles)
int N = 15; //total population size
int n = 5; //sample size of 5
Hypergeometric X = Hypergeometric(K, N, n);
std::cout << X.P(3) << std::endl; //0.3996

Common errors

Hypergeometric X = Hypergeometric(5, 15, 2);
std::cout << X.P(-1) << std::endl; //Error: Number of successes in sample cannot be less than 0 or more than the sample size or more than the number of successes in population.

Good to know: k cannot be negative and has a max value of min(n, K).