There is a 50 chance of making 0 40 chance of making 100 and

There is a 50% chance of making $0, 40% chance of making $100, and a 10% chance of losing $100. Calculate the expected value and variance of the payoff.

Solution

Expected value = 50% x $0 + 40% x $100 - 10% x $100 = 0 + $40 - $10 = $30

Variance ($) = 50% x [(0 - 30)²] + 40% x [(100 - 30)²] + 10% x [(-100 - 30)²]

= 50% x 900 + 40% x 4,900 + 10% x 16,900

= 450 + 1,960 + 1,690 = $4,100