<\/span><\/h2>\n\nTo find the expected value of a probability model, follow these steps:<\/b><\/p>\n
1. Identify the random variable: Determine the variable or outcome of interest in the probability model.<\/p>\n
2. List all possible values of the random variable: Create a comprehensive list of all the potential outcomes that the random variable can take.<\/p>\n
3. Assign probabilities to each value: Determine the probability associated with each value of the random variable. These probabilities should sum up to 1.<\/p>\n
4. Multiply each value by its corresponding probability: Multiply each possible value of the random variable by its probability.<\/p>\n
5. Sum up the products: Add up all the products obtained in the previous step.<\/p>\n
6. The resulting sum is the expected value: The final value obtained after summing up the products is the expected value of the probability model.<\/p>\n
Example:<\/b>
\nSuppose you are rolling a fair six-sided die, and we are interested in finding the expected value of the number rolled.<\/p>\n
1. Identify the random variable: The random variable is the number rolled on the die.<\/p>\n
2. List all possible values of the random variable: The possible values are 1, 2, 3, 4, 5, and 6.<\/p>\n
3. Assign probabilities to each value: Since the die is fair, each value has a probability of 1\/6.<\/p>\n
4. Multiply each value by its corresponding probability: Multiply 1 by 1\/6, 2 by 1\/6, and so on.<\/p>\n
5. Sum up the products: Add the results from the previous step: (1 \u00d7 1\/6) + (2 \u00d7 1\/6) + (3 \u00d7 1\/6) + (4 \u00d7 1\/6) + (5 \u00d7 1\/6) + (6 \u00d7 1\/6) = 3.5<\/p>\n
6. The expected value is 3.5: In this case, the expected value of the probability model is 3.5.<\/p>\n