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:
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: 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; //0.3996Last updated