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# Binomial distribution, probability density function, cumulative distribution function, mean and variance

This calculator calculates probability density function, cumulative distribution function, mean and variance of a binomial distribution for given n and p

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In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: a random variable containing single bit of information: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q = 1 − p). Wikipedia

Probability density function: $f(x;p,n) = C^{n}_x (p)^x (1-p)^{n-x}$,
Cumulative distribution function: $F(x;p,n) = \sum_{i=0}^{x}{C^{n}_i (p)^{i}(1 - p)^{(n-i)}}$
where
$C^{n}_x=\frac{n!}{(n-x)!x!}$ - binomial coefficient

Mean, or expected value of a binomial distribution is equal to $\mu_x=np$, and the variance is equal to $\sigma^{2}_{x}=np(1-p)$

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 probability density function, cumulative distribution function, mean and variance for given p and n.

### Binomial distribution

Digits after the decimal point: 4
Expected value

Variance

Probability density function
Cumulative distribution function