## Binomial distribution: mean and variance

A Bernoulli random variable with parameter $p$ is a random variable that takes on the values $0$ and $1$, where $1$ happens with probability $p$ and $0$ with a probability of $1-p$. If $X_1,\dots,X_n$ are $n$ independent Bernoulli random variables, we define $$X = X_1 + \cdots + X_n.$$ The random variable $X$ is said […]