Binomial Distribution

Tags

PAS

Cegep/2

Word count

80 words

Reading time

1 minute

Discrete probability distribution of the number of successes in $n$ Bernoulli trials with replacement
Sym. $B(n,p)$

Properties

$$\begin{array}{rl}P(X=k)& =(\genfrac{}{}{0ex}{}{n}{k})p^k(1-p{)}^{n-k}\\ E(X)& =np\\ Var(X)& =np(1-p)\end{array}$$

Unlike hypergeometric distribution, since the experiments are conducted with replacement, the PMF doesn't depend on population size and number of successes in population.

Contributors

Ajitani Hifumi

Changelog

Last edited about 2 hours ago

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