Suppose X is a random variable which follows Bin10p where 0

Suppose X is a random variable which follows Bin(10,p), where 0<p<1.

Find the value of p for which V(X) is as large as possible.

Show detailed steps please.

Solution

As

V(x) = n p (1 - p)

Optimizing V(x) by setting V\'(x) = 0,

V\'(x) = n [(1-p) + (-p)] = 0

Cancelling n,

1 - 2p = 0

p = 1/2 [ANSWER]