All of the above examples look at a discrete random variable. Now plug these values and probabilities into the expected value formula and end up with: -2 (5/6) + 8 (1/6) = -1/3. If in the long run, you won't lose any money, then the carnival won't make any. The possible values are -$1 for losing and $999,999 for winning (again we have to account for the cost to play and subtract this from the winnings). ", ThoughtCo uses cookies to provide you with a great user experience. Courtney K. Taylor, Ph.D., is a professor of mathematics at Anderson University and the author of "An Introduction to Abstract Algebra. In the short term, the average of a random variable can vary significantly from the expected value. For the same entry fee of $2, if the number showing is a six then you win $12, otherwise, you win nothing. You should either list these or create a table to help define the results. However, it is possible to define the expected value for a continuous random variable as well. In such a case, the EV can be found using the following formula: Where: 1. The return on the investment is an unknown variable that has different values associated with different probabilities.. On the other hand, Project Y is expected to achieve a value of $2.5 million, with a probability of 0.4 and achieve a value of $1.5 million, with a probability of 0.6. If the number showing is a six you win $10, otherwise, you win nothing. Although millions can be won for the price of a $1 ticket, the expected value of a lottery game shows how unfairly it is constructed. The expected value can really be thought of as the mean of a random variable. As another example, consider a lottery. A real-life example will likely assess the Net Present Value (NPV)Net Present Value (NPV)Net Present Value (NPV) is the value of all future cash flows (positive and negative) over the entire life of an investment discounted to the present. The concept is frequently used with multivariate models and scenario analysisScenario AnalysisScenario analysis is a process of examining and evaluating possible events or scenarios that could take place in the future and predicting the. A long-run average value of random variables, Scenario analysis is a process of examining and evaluating possible events or scenarios that could take place in the future and predicting the. This means that over the long run, you should expect to lose on average about 33 cents each time you play this game. An independent variable is an input, assumption, or driver that is changed in order to assess its impact on a dependent variable (the outcome). The value of this outcome is -2 since you spent $2 to play the game. However, NPV calculations also consider the EV of different projects. You're at a carnival and you see a game. Both 0 and 00 are green. Here if you bet $1 and the ball lands on a red number in the wheel, then you will win $2. EV– the expected value 2. But you will lose more often. Note that the example above is an oversimplified one. To begin, you must be able to identify what specific outcomes are possible. In such a scenario, the EV is the probability-weighted averageof all possible events. One of the simplest bets is to wager on red. ., xn with probabilities p1, p2, . . Certified Banking & Credit Analyst (CBCA)™, Capital Markets & Securities Analyst (CMSA)™, Financial Modeling and Valuation Analyst (FMVA)™, Financial Modeling and Valuation Analyst (FMVA)®, Financial Modeling & Valuation Analyst (FMVA)®. Therefore, the general formula to find the EV for multiple events is: You are a financial analystFinancial Analyst Job DescriptionThe financial analyst job description below gives a typical example of all the skills, education, and experience required to be hired for an analyst job at a bank, institution, or corporation. To answer a question like this we need the concept of expected value. The expected value of this game is -2 (5/6) + 10 (1/6) = 0. In such a case, the EV can be found using the following formula: However, in finance, many problems related to the expected value involve multiple events. The first variation of the expected value formula is the EV of one event repeated several times (think about tossing a coin). Yes, you will win sometimes. The EV can be calculated in the following way: EV (Project A) = [0.4 × $2,000,000] + [0.6 × $500,000] = $1,100,000, EV (Project B) = [0.3 × $3,000,000] + [0.7 × $200,000] = $1,040,000. In the same way as before we can calculate the expected value of games of chance such as roulette. The Normal Approximation to the Binomial Distribution, Expected Value of a Binomial Distribution, Use of the Moment Generating Function for the Binomial Distribution, B.A., Mathematics, Physics, and Chemistry, Anderson University. To find the expected value of a game that has outcomes x1, x2, . NPV analysis is a form of intrinsic valuation and is used extensively across finance and accounting for determining the value of a business, investment security, of the projects instead of their EV. In such a scenario, the EV is the probability-weighted average of all possible events. Here the house has a slight edge (as with all casino games). NPV analysis is a form of intrinsic valuation and is used extensively across finance and accounting for determining the value of a business, investment security, Join 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari, A dependent variable is a variable whose value will change depending on the value of another variable, called the independent variable. The expected value can really be thought of as the mean of a random variable. CFI is the official provider of the Financial Modeling and Valuation Analyst (FMVA)™FMVA® CertificationJoin 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari certification program, designed to transform anyone into a world-class financial analyst. Therefore, your company should select Project A. It is directly related to the concept of expected returnExpected ReturnThe expected return on an investment is the expected value of the probability distribution of possible returns it can provide to investors. What Are the Odds of Winning the Lottery? Expected value is a commonly used financial concept. All that we must do in this case is to replace the summation in our formula with an integral. . The variable is not continuous and each outcome comes to us in a number that can be separated out from the others. The expected value is what you should anticipate happening in the long run of many trials of a game of chance. The financial analyst job description below gives a typical example of all the skills, education, and experience required to be hired for an analyst job at a bank, institution, or corporation. The carnival game mentioned above is an example of a discrete random variable. There is a 20/38 probability of losing your initial bet of $1. Net Present Value (NPV) is the value of all future cash flows (positive and negative) over the entire life of an investment discounted to the present. The EV of Project A is greater than the EV of Project B. Project B shows a probability of 0.3 to be valued at $3 million and a probability of 0.7 to be valued at $200,000 upon completion. Using the expected value formula, we will multiply each event with its probability and add them all up for each fund. For $2 you roll a standard six-sided die. By using ThoughtCo, you accept our, How to Calculate Expected Value in Roulette. In order to select the right project, you need to calculate the expected value of each project and compare the values with each other. The math behind this kind of expected value is: The probability (P) of getting a question right if you guess: .25 The number of questions on the test (n)*: 20 P x n = .25 x 20 = 5 *You might see this as X instead. This means that if you ran a probability experiment over and over, keeping track of the results, the expected value is the average of all the values obtained. This gives us an expected value of: (-1)(12,271,511/12,271,512) + (999,999)(1/12,271,512) = -.918. A zero sum game is a situation where losses incurred by a player in a transaction result in an equal increase in gains of the opposing player. It can be utilized to assess the strength of the relationship between variables and for modeling the future relationship between them. According to estimates, Project A, upon completion, shows a probability of 0.4 to achieve a value of $2 million and a probability of 0.6 to achieve a value of $500,000. A ball randomly lands in one of the slots, and bets are placed on where the ball will land. So if you were to play the lottery over and over, in the long run, you lose about 92 cents — almost all of your ticket price — each time you play. Half of the 1-36 are red, half are black. . Now suppose that the carnival game has been modified slightly. P(X)– the probability of the event 3. n– the number of the repetitions of the event However, in finance, many problems related to the expected value involve multiple events. , pn, calculate: For the game above, you have a 5/6 probability of winning nothing. In the long run, you won't lose any money, but you won't win any.