![]() We would calculate the expected value for winnings to be: Expected value = 0.2*1 + 0.7*2 + 0.1*3 = 1.9 inchesĮxpected value is often used by gamblers to determine how much they could potentially win at a certain game.įor example, suppose in a certain game there is a 5% chance of winning $100, a 50% chance of winning $0, and a 45% chance of losing $20.We would calculate the expected value for the amount of rain to be: Example 2: WeatherĮxpected value is often used by agricultural companies to determine the expected amount of rain that will fall during a given season.įor example, suppose a there is a 20% chance of 1 inch of rain, a 70% chance of 2 inches of rain, and a 10% chance of 3 inches of rain. This means that if we invested in this particular investment an infinite number of times, we would expected a long-term average annual return of 3.75%. This particular investment has a positive expected value. ![]() We would calculate the expected value of this investment to be: Example 1: InvestmentsĮxpected value is often used by trading firms to determine the expected profit or loss from some investment.įor example, suppose a particular investment is could deliver a 5% annual return with a probability of 0.95, but it could also deliver a -20% annual return with a probability of 0.05. The following examples show how expected value is calculated in five different real-world situations. That formula might look a bit confusing, but it will make more sense when you see it used in the context of actual examples. We use the following formula to calculate the expected value of some event: Expected value is a value that tells us the expected average that some random variable will take on in an infinite number of trials. ![]()
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