Calculating the expected value

The formula for the expected value is equal to the sum of the product of each conceivable result with its probability.

The expected value for a random variable X is given by:

or

Example 1:

Find the expected value for the following probability distribution using the expected value formula.

Apply the expected value formula to find the answer:

Answer: 2.75

Example 2:

If you roll an odd number, you will be paid $1, and if you roll an even number, you will be rewarded $2. Calculate the predicted monetary value of a single die roll.

The sample space of the experiment is {1,2,3,4,5,6}.

The table illustrates the probability distribution for a single roll of a die and the amount that will be paid for each outcome.

Use the expected value formula:

Answer: $1.50 (on average, you get $1.50 per roll)