CAT / FIA FMA Syllabus B. Data Analysis And Statistical Techniques - Expected Values - Notes 6 / 7
What is an expected value?
Expected values are used in decision making when there are many possible outcomes and each outcome has a probability attached to it.
It is an expected value/outcome if the decision will be made.
E.V. = Σ (Each possible outcome x Probability)
Illustration
An ice cream salesman has varying levels of demand for his sales and probabilities for each level of demand occurring. (Table below)
What is the expected value of revenue for the ice cream salesman?
| Demand | Sales ($) | Probability |
|---|---|---|
| High | 500,000 | 0.2 |
| Medium | 300,000 | 0.5 |
| Low | 200,000 | 0.3 |
| 1 |
Solution
E.V. = Σ (Each possible outcome x Probability)
=(500,000 x 0.2) + (300,000 x 0.5) + (200,000 x 0.3)
= 310,000
Assumptions/Features of E.V.
The decision will be taken many times.
It ignores the investor's attitude to risk, as it is an average of all of the outcomes occurring based on their probability.