Mean and variance of a binomial

Problem

Compute the mean and variance of $X\sim B(20;\,0{,}3)$.

Solution

For the binomial $\mu = np$ and $\sigma^2 = np(1-p)$, with $n=20$ and $p=0{,}3$: $\mu = 20\cdot 0{,}3 = \boxed{6}, \qquad \sigma^2 = 20\cdot 0{,}3\cdot 0{,}7 = \boxed{4{,}2}.$ The standard deviation is $\sigma = \sqrt{4{,}2}\approx 2{,}05$.

Links

Topics: Distribuzioni probabilita
Concepts: Distribuzione binomiale · Valore atteso · Varianza
Methods: Valore atteso
Skills: Usare formule
Exercise type: Calcolo espressioni