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Binomial distribution

The binomial distribution $\text{Bin}(n, p)$ describes the number of successes in $n$ independent trials where each trial has success probability $p$ , such as the number of defects in a sample with replacement. The expected value is simple to compute directly from $n$ and $p$ .

E[X] = np

expected number of successes

X \sim \text{Bin}(n, p)

n

independent trials, success probability

p

Symbols

$n$	number of trials
$p$	success probability per trial
$X$	number of successes

Example

$X \sim \text{Bin}(10,\ 0.5)$ :

$E[X] = 10\cdot 0.5 = 5$ .

Use the binomial distribution when each trial is independent with the same success probability.

Practise distributions for free →

← Normal distribution and z-score · Poisson and exponential distribution →

Part of Statistics and Risk Analysis: Distributions.