The binomial distribution gives the frequencies of "successes" in a fixed number of independent "trials". Use this tag for questions about data that might be binomially distributed or for questions about the theory of this distribution.

Overview

The binomial distribution gives the frequencies of "successes" in a fixed number of independent "trials". It is a discrete distribution parametrized by $p$, the probability of "success" in a trial. For $k$ "successes" in $n$ "trials" ($k \leq n$), the form of the probability mass function is:

$$P(k,n;p) = {n \choose k} p^k (1-p)^{n-k}$$

For a binomially distributed variable $X$, the expected value and variance are given by:

$$\mathrm{E}[X] = np $$ $$\mathrm{Var}[X] = np(1-p) $$

A common example to demonstrate the use of the demonstration is finding the probability of the number of heads or tails in a certain number of coin flips.

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