Suppose a fair, two-sided coin is flipped. If it comes up heads you receive $5; if it comes up tails you lose $1. The variance of this lottery is
A) 4.5
B) 9.0
C) 13.5
D) 18.0

Question

Quizplus · Accepted Answer

The expected value of this lottery is:
(0.5)(5) + (0.5)(-1) = $2
The variance can be calculated using the formula:
Var(X) = E[(X - E(X))^2]
= E[(X^2) - 2XE(X) + (E(X))^2]
Notice that X can only take on two possible values: 5 and -1. Therefore:
Var(X) = [(5)^2(0.5) + (-1)^2(0.5)] - 2(2)(0.5) + (2)^2
= 22 - 2 + 4
= 24 - 2
= 22
So the variance of the lottery is 22.
The only answer choice that matches this calculation is B (9.0 is not even close, and 13.5 and 18.0 are both too high).

Suppose a Fair, Two-Sided Coin Is Flipped