No links please Q In a Binomial (a, p) distribution show that σx2 μ (where σx2 is variance and - Maths - Probability

Question

No links please
Q In a Binomial (a, p) distribution show that σ x 2 <
μ (where σ x 2 is variance and μ is mean of this
distribution)

Varun Rawat · Accepted Answer

Let X be a binomial variate with parameters n and p
 Then,Meanμ = np and Varianceσ2 = npqmean - variance = np - npq = np1-q = np2⇒mean - variance > 0     as, n∈N and p > 0, so np2 > 0⇒mean > variance⇒μ > σ2

No links please Q. In a Binomial (a, p) distribution show that σ x 2 < μ (where σ x 2 is variance and μ is mean of this distribution).

No links please
Q. In a Binomial (a, p) distribution show that ${σ_{x}}^{2} < μ$ (where $σ x^{2}$ is variance and $μ$ is mean of this distribution).