Qa - binomial distributions

x ~ B(n,p)

x ~b(16,P)

p = 1/2

q = 1/2

sd = root npq

     = root 16*1/2*1/2

     =root 4

     =2

(sd)^2 = variance

(2)^2 = variance = 4

variance is np(1-p) os we have to find the least value of p*(1-p)  p(1-p) = p - p^2. for this function the maximum value is 0.25 which it will attain at p = 0.5. and minimum value is attained at p =0 or p=1 which is 0,. (the function is an inverted parabola so it will have a maximum but the boundaries of the interval are the minimum values) which is 0 so least value is 0 maximum value is 4

Thanks for the answers. 4 will be the maximum variance (n/4). For minimum variance i got 0, but the answer given was 2. Hence got the doubt...