# Binomial random variable

• Feb 23rd 2010, 07:28 PM
whatsanihar
Binomial random variable
Let X be a Binomial random variable with parameters n; . Prove the
expectation and variance of X are n(pi) and n(1-pi) respectively. (Hint: use
the defi…nition of expectation and variance and the relation between Bernoulli
and Binomial.

So E(x) = sum(xP(x)) and Var(x) = sum((x-u)^2*P(x))

Not really sure where to go from here. P(x) for binomial is equal to n!/x!(n-x)!*pi^x*(1-pi)^(n-x)
• Feb 23rd 2010, 08:30 PM
cpbrunner
Remember that a binomial R.V. is simply the sum of $n$ independent Bernoulli trials. Also recall that:
$E(\sum X)=\sum E(X)$
This should help you figure out those expectations.