Binomial Distribution

Binomial distribution0 / 4

1. Bernoulli trialsTrials are Bernoulli when there is a fixed number of them, each has only success or failure, they are independent, and the chance of success stays the sameStart
2. The binomial probabilityIf $X \sim B(n, p)$, then $P(X = r) = {}^nC_r\,p^r q^{n - r}$ with $q = 1 - p$, for $r = 0, 1, \dots, n$Locked
3. At least, at most and word problemsAdd the needed terms, or use the complement: $P(X \ge 1) = 1 - q^n$; read $n$,
4. Mean and variance of a binomial distribution$E(X) = np$ and $\text{Var}(X) = npq$; from a given mean and variance, $q = \dfrac{\text{Var}}{\text{mean}}$,