# Tagged: Bernoulli random variable

## Problem 748

Suppose that $X$ is a random variable with Bernoulli distribution $B_p$ with probability parameter $p$.

Assume that the variance $V(X) = 0.21$. We further assume that $p > 0.5$.

(a) Find the probability $p$.

(b) Find the expectation $E(X)$.

## 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 $X$.