Binomial

Represents the number of successes in a fixed number of independent and identically distributed Bernoulli trials (each trial having two possible outcomes: success or failure)

Create a new Binomial distribution

Binomial X = Binomial(n, p); 

creates a discrete Binomial probability distribution.

Distribution properties:

Property	Type/Return type	Description
n	int	Number of executed events
p	double -> [0, 1]	Probability of a succesful event
E()	double	Returns the expected value of succesful events after executing n independend events, all with constant probability of p.
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 obtaining exactly 𝑘 successes in 𝑛 trials: P(X = k)
P_LT(int k)	double	Probability of obtaining less than 𝑘 successes in 𝑛 trials: P(X < k)
P_LTE(int k)	double	Probability of obtaining less than or exactly 𝑘 successes in 𝑛 trials: P(X ≤ k)
P_HT(int k)	double	Probability of obtaining more than 𝑘 successes in 𝑛 trials: P(X > k) = P(X ≤ k)
P_HTE(int k)	double	Probability of obtaining more than or exactly 𝑘 successes in 𝑛 trials: P(X ≥ k) = P(X < k)

Example

Example of a binomial distribution

//Example: what's the probability of getting exactly 5 heads 
//when flipping a coin 10 times?
double p = 0.5; //probability of getting heads is 50%
int n = 10; //10 independed events
Binomial X = Binomial(n, p);
std::cout << X.P(5) << std::endl; //0.246094

Common errors

Binomial X = Binomial(25, -0.5); //Error: Probability cannot be less than 0 or more than 1.
std::cout << X.P(30) << std::endl; //Error: The number of succesful trials cannot exceed the number of all trials or be less than 0.  

Good to know: k cannot exceed the number of executed events and probability p cannot be outside the bounds of [0, 1].