Problem 3 Using your stellar calculus skills show that the v

Problem 3: Using your stellar calculus skills, show that the variance of the binomial distribution is maximized at p
= 0.50.

Solution

As

V(x) = n p (1 - p) = n p - np^2

When we optimize, we set the derivative to 0:

V\'(x) = n - 2np = 0

Cancelling n,

1 - 2p = 0

p = 1/2

Also, by second derivative test,

V\'\'(x) = -2n < 0, which means this is a maximum.

Thus, the binomial distrbution\'s variance is maximized at p = 1/2. [ANSWER]