What is the Expected Value?
The expected value, also known as the mean value, is the total of all potential decision outcomes multiplied by each possibility's probability. Or to put it another way, it is the benefit you would anticipate if you repeatedly made the same choice under the same circumstances.
Formula:
The formula for the expected value in statistics is as follows:
E (X) = Expected value
∑ = sum of an outcomes
µ_{x } = Mean
X = an outcome
P (X) = probability of an outcome
The advantages of estimating the expected value:
A crucial tool for assisting people, companies, and organizations in making wise decisions is the expected value. Here are some advantages of estimating anticipated value:
Helps You Make Knowledgeable Decisions:
Based on prior events, expected value aids in forecasting an event's result. Decisions regarding future occurrences may be made by people and corporations by assessing the expected value.
Reduces dangers:
By estimating the probability of various events, the expected value can assist in reducing risks. Businesses may evaluate the likelihood of success or failure and take the necessary precautions to reduce risks by estimating the expected value.
Boosts Profits:
By making wise investments and other financial decisions, the expected value may assist firms in maximizing earnings. The expected value is determined. By calculating the expected value, businesses can determine the probability of success or failure and invest accordingly.
Example section:
In this section, we'll cover the method of calculating the expected value.
Example 1:
Find the expected value for the following probability distribution using the expected value formula.
X = 1, 2, 3, 4, 5
P (X) = 0.50, 0.20, 0.30, -0.20, -0.10
Solution:
Using the expected value formula:
x | P(x) | xP(x) |
1.00 | 0.50 | 0.50 |
2.00 | 0.20 | 0.40 |
3.00 | 0.30 | 0.90 |
4.00 | -0.20 | -0.80 |
5.00 | -0.10 | -0.50 |
∑x = 15.00 | ∑P(x) = 0.70 | ∑xP(x) = 0.50 |