Expected value

Definition

Expected value is the weighted average of all possible outcomes of a random variable, where each outcome is weighted by its probability. It provides a measure of the center or 'expected' outcome of a probability distribution.

5 Must Know Facts For Your Next Test

1. Expected value is calculated by summing the products of each possible outcome and its corresponding probability.
2. It is used in finance to predict future values based on historical data and probability distributions.
3. An expected value does not guarantee any specific outcome; it represents an average over many trials.
4. In investment analysis, expected value helps in assessing the risk and return of various financial instruments.
5. The Law of Large Numbers states that as more trials are conducted, the sample mean will converge to the expected value.

Review Questions

• How do you calculate the expected value for a discrete random variable?
• Why is expected value important in making financial decisions?
• What does the Law of Large Numbers imply about expected value?

Related terms

Probability Distribution: A function that describes the likelihood of various outcomes in an experiment.

Variance: A measure of how much values in a dataset differ from the mean.

Standard Deviation: The square root of variance, indicating how spread out numbers are around the mean.