# Variance of Binomial distribution

Can somebody plz xplain the derivaton of variance of Bino.Dist

Var = np(1-p)

Normally Variance is p(X-Expextedreturn or Mean)^2

It’s the same here, but it’s rather complicated.

_σ_² = Σ P(i)(iμ

= (_n_C0)(p^0)[(1 – p)^n](0 – np)² + (_n_C1)(p^1)[(1 – p)^(n–1)](1 – np)² + ∙ ∙ ∙ + (n_C_n)(p^n)[(1 – p)^0](nnp

If you add all this up, it equals np(1 – p)

Trust me on this: you don’t want to see the rest of the algebra.

if you need derivations go refer to a statistics text book.

http://www.math.ubc.ca/~feldman/m302/binomial.pdf

Yes, the long derivation is a pig. As S2000magician and cpk123 have demonstrated, the algebra gets real ugly real fast.

Given that the binomial is just the sum of n independent and identically distributed Bernoulli random variables, then you can take advantage of the fact the variance will simply be n x Var(Bernoulli). The variance of a Bernoulli random variable is just p(1-p), so the variance of the binomial will be n * p *(1-p)