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# Binomial distribution. Probability-density function

##### Binomial distribution, probability-density function calculation
Timur2015-08-16 13:29:01

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
Probability-density function:

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