<\/span><\/h2>\nTo find the expected value of a distribution, follow these steps:<\/p>\n
1. **Identify the random variable:** Determine the random variable that represents the outcomes of interest in your distribution. For example, if you are working with the distribution of the outcomes of rolling a fair six-sided die, the random variable would be the numbers 1 through 6.<\/p>\n
2. **Assign probabilities:** Assign probabilities to each possible outcome of the random variable. The sum of all these probabilities should equal 1. For the fair six-sided die example, each outcome has a probability of 1\/6.<\/p>\n
3. **Multiply each outcome by its probability:** Multiply each outcome of the random variable by its corresponding probability. This step helps to weigh the outcomes based on their likelihood of occurring.<\/p>\n
4. **Sum up the products:** Add up all the product values obtained from the previous step. This will provide the expected value of the distribution.<\/p>\n
As a mathematical formula, the expected value (E) can be represented as:<\/p>\n
E = x1*p1 + x2*p2 + x3*p3 + … + xn*pn<\/p>\n
Here, x1, x2, x3, …, xn represent the possible outcomes of the random variable, and p1, p2, p3, …, pn are their respective probabilities.<\/p>\n