Question

You are playing a game with a friend where you flip a coin and if it comes up heads you give her 1 dollar and if it comes up tails she gives you one dollar. What would be the variance of your earnings?

Answer 1

Let x = number of times it comes up tails.

then x follows a binomial distribution (n, p) where n is the nuber of times you flip and p = P(T) on a flip.

your earnings will be x - (n-x) = 2x-n

Variance of binomial r.v. is n*p*(1-p).

variance of a constant is 0.

you need the VAR(2x-n) = VAR(2x)-VAR(n) = VAR(2x) = 4*VAR(x) = 4*n*p*(1-p)