Question

3. If X - B (n, p), what would be the greatest value of the variance of x when n = 16?
(a) 2.
(b) 4.
(C) 8.
(d) √5​

Answer 1

Given :  X - B (n, p), , n = 16

To Find : what would be the greatest value of the variance of x

Solution:

Variance = npq

n = 16

=> variance = 16pq

q = 1 - p

=> variance = 16p(1 - p)

=> variance = 16(p - p²)

V =  16(p - p²)

dV/dp  = 16( 1 - 2p)

dV/dp  = 0

=> 16( 1 - 2p) = 0

=> p = 1/2

d²V/dP² = 16(0 - 2)

=> d²V/dP² = -32 < 0

hence variance is maximum when p = 1/2

p = 1/2  => q = 1/2

variance = 16pq  

= 16(1/2)(1/2)

= 4

greatest value of the variance of x when n = 16  is 4

option b is correct

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