Question

(a) Prove that for the binomial
distribution with parameter n and p, variance cannot exceed n/4​

Answer 1

Answer:

Let X be a binomial variate with parameters n and p. Then,

Mean = np

And, Variance = npq

Mean - Variance = np−npq=np(1−q)=np

2

Mean−Variance>0 [n∈N,p>0,therefore,np

2

>0]

Mean>Variance

HOPE ITZ CLEAR....