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

Source:

• 202009011233 Statistics - Khan Academy

Tags:

• statistics
• probabilities

Relevant:

• 113.036 Statistics - Expected Value