Expected value example for a concert promoter and the weather

A concert organizer wants to throw a concert - Costs = $50,000 - Revenue | good weather = $200,000 - Revenue | moderate weather = $80,000 - Revenue | bad weather = $0 - P(good weather) = 20% - P(moderate weather) = 30% - P(bad weather) = 50%

Here’s how to tell if they should go forward with the event - E(X) = (200,000 * .2) + (80,000 * .3) + (0 * .5) = $64,000 - $64 (expected revenue) > $50 (costs) so they should go ahead

Here’s how to get the variance and standard deviation (the most likely range of outcomes) - Variance = ((200,000 * .2)^2 * .2) + ((80,000 * .3)^2 * .3) + ((0 * .5)^2 * .5 = 5,824,000,000 - Standard Deviation = \sqrt{5,824,000,000} = $76,315