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
P_Y (k) = \frac{n!}{(n-k)!k!} p^k q^{n-k}, where
\frac{n!}{(n-k)!k!} - binomial coefficient and q=1-p

Mathematical expected value having a binomial distribution is equal to
M(Y)=np, and the dispersion is equal to D(Y)=npq

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.


Binomial distribution

Digits after the decimal point: 2
Probability-density function
Expected value