Expected value predicts the value of a random variable.
Expected value is a statistical concept that expresses the best prediction of a random variable x. It can be thought of as the average or central value of x, where x can vary in a probabilistic manner. The concept of expected value is used in the business world to estimate likely gains or losses from a business venture.
Instructions
1. Create two columns in which you will enter the numbers needed to calculate expected value. You can do this either in a spreadsheet program or on a piece of paper.
2. Enter the values that the variable x can take in the first column. For example, suppose x is the number of children that families have in a particular town. Assume x varies from 0 to 5 (i.e, people have between zero and five children in that town), and write down the numbers 0 to 5 in the first column, with 0 in the first row and 5 in the last.
3. Enter the fraction of families having a given number of children in the second column. In this example, this information will come from census data. For instance, if 18 percent of families have no children, enter 0.18 in the first row of the second column. If 39 percent of families have one child, enter 0.39 in the second row of the second column, and so on down the column. Thus, the second column contains the probabilities that families will have a specific number of children in that town.
4. Create another column alongside the first two columns. Multiply the entries in the first and second columns and enter the products in the third column, where each entry in that column will be the product of the entries in the other two columns from that same row. In this example, the first entry in the third column will be 0 (i.e., 0 times 0.18) and the second entry will be 0.39 (i.e., 1 times 0.39).
5. Add all the entries in the third column. In our example, we would add 0, 0.39 and the other entries in the third column that we calculated in the previous step. The sum is the expected value of x. This means that if a family were to be picked at random from that town, the sum calculated in this step would be the number of children we would expect them to have.
Tags: number children, second column, third column, children that, families have