To calculate expected value, enter the potential outcome, associated probability, and click 'Calculate'.
The expected value calculator helps you to calculate expected value, which is the average prediction of a probability distribution.
The expected value is the average of the possible outcomes of a random variable or event ‘X’, weighted by their probabilities ‘P(X)’.
Steps include:
Mathematically;
\(\text{Expected Value Formula}=\sum P\left(X_{i}\right) . X_{i}\)
Suppose you play a game that involves rolling a fair six-sided die. The payouts and probabilities for each outcome are as follows:
Outcome (x) | Payout ($) | Probability (P(x)) |
---|---|---|
1 | -2 | 1/6 |
2 | 0 | 1/6 |
3 | 2 | 1/6 |
4 | 4 | 1/6 |
5 | 6 | 1/6 |
6 | 8 | 1/6 |
Step 01: Multiplying Each Outcome by Its Weighted Probability
\(EV = (-2 \times \frac{1}{6}) + (0 \times \frac{1}{6}) + (2 \times \frac{1}{6}) + (4 \times \frac{1}{6}) + (6 \times \frac{1}{6}) + (8 \times \frac{1}{6})\)
Step 2: Calculating Individual Products
\(EV = \left(-\frac{2}{6}\right) + \left(0\right) + \left(\frac{2}{6}\right) + \left(\frac{4}{6}\right) + \left(\frac{6}{6}\right) + \left(\frac{8}{6}\right)\)
Step 3: Taking the Sum of All the Values
\(EV = \frac{-2 + 0 + 2 + 4 + 6 + 8}{6} = \frac{18}{6} = 3\)
Our calculator serves different purposes under conditions where probabilistic decision-making is very important. Some of these include:
Expected value calculation helps us to predict the expected average when a risk is taken with an uncertain outcome.
Yes, it can be. If calculated expected number is negative, it means you are likely get an average loss, which is unfavorable.
DeGroot, M.H. and Schervish, M.J. (2012) Probability and Statistics. 4th edn. Boston, MA: Pearson Education. Available at: https://www.pearson.com/store/p/probability-and-statistics/P100000617944
Feller, W. (1968) An Introduction to Probability Theory and Its Applications. 3rd edn. New York: Wiley. Available at: https://www.wiley.com/en-us/An+Introduction+to+Probability+Theory+and+Its+Applications%2C+Volume+1%2C+3rd+Edition-p-9780471257080
Ross, S.M. (2014) Introduction to Probability Models. 11th edn. Amsterdam: Academic Press. Available at: https://www.elsevier.com/books/introduction-to-probability-models/ross/978-0-12-407948-9
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