## Expectation, Variance, and Standard Deviation of Bernoulli Random Variables

## Problem 747

A random variable $X$ is said to be a **Bernoulli random variable** if its probability mass function is given by

\begin{align*}

P(X=0) &= 1-p\\

P(X=1) & = p

\end{align*}

for some real number $0 \leq p \leq 1$.

**(1)** Find the expectation of the Bernoulli random variable $X$ with probability $p$.

**(2)** Find the variance of $X$.

**(3)** Find the standard deviation of $X$.