
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(1pi) 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((xu)^2*P(x))
Not really sure where to go from here. P(x) for binomial is equal to n!/x!(nx)!*pi^x*(1pi)^(nx)

Remember that a binomial R.V. is simply the sum of $\displaystyle n$ independent Bernoulli trials. Also recall that:
$\displaystyle E(\sum X)=\sum E(X)$
This should help you figure out those expectations.