Calculating the expected value

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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:

Expected value for a random variable X


Expected value for a random variable X another

Example 1:

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

Example expected value 1

Apply the expected value formula to find the answer:

Example expected value result

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.

Example expected value 2

Use the expected value formula:

Example expected value 2 result

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