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

Var = np(1-p)

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

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*)(*i* – *μ*)²

= (_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](*n* – *np*)²

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.

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)