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ProfessionalStatistics# Binomial distribution. Probability-density function

##### Binomial distribution, probability-density function calculation

**Binomial distribution**- the probability distribution of the number of occurrences of an event in repeated independent tests. If the occurence number of an event equals p, moreover, p can belong to the interval [0;1], then the Y number of event occurance with n independent tests is a random variable taking values of k = 1, 2, ...., n with probabilities

, where

- binomial coefficient and

Mathematical expected value having a binomial distribution is equal to

, and the dispersion is equal to

If the number n is rather big, then binominal distribution practically equal to the normal distribution with the expected value np and dispersion npq.

This calculator calculates P(k) and makes distribution graph for a given p and n.

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