Expected value

Definition

Expected value is a fundamental concept in probability that represents the average outcome of a random event over a large number of trials. It is calculated by multiplying each possible outcome by its probability and summing the results.

5 Must Know Facts For Your Next Test

1. Expected value is also known as the mean or expected average.
2. It can be applied to both discrete and continuous random variables.
3. The formula for expected value (E) in a discrete setting is E(X) = Σ [x * P(x)], where x is an outcome and P(x) is its probability.
4. In real-world applications, expected value helps in decision-making processes like risk assessment and investment strategies.
5. Even if individual outcomes are highly variable, the expected value provides a single summary measure of central tendency.

Review Questions

• What is the formula for calculating the expected value of a discrete random variable?
• How does expected value assist in making decisions involving uncertainty?
• Can the expected value be applied to continuous random variables, and if so, how?

Related terms

Probability Distribution:

A function that describes the likelihood of different outcomes in an experiment.

Variance:

A measure of how much values in a data set differ from the mean; it quantifies variability.

Random Variable: A variable whose possible values are numerical outcomes of a random phenomenon.