Expected value

Definition

Expected value is the weighted average of all possible values that a random variable can take on, with weights being their respective probabilities. It provides a measure of the center of the distribution of the variable.

5 Must Know Facts For Your Next Test

1. Expected value is often denoted by $E(X)$ or $\mu$.
2. In linear regression, expected value helps in predicting the mean response variable given certain predictor values.
3. For a discrete random variable, expected value is calculated as $E(X) = \sum{[x_i \cdot P(x_i)]}$ where $x_i$ are outcomes and $P(x_i)$ are their probabilities.
4. In continuous cases, it is computed using integrals: $E(X) = \int{x \cdot f(x)dx}$ where $f(x)$ is the probability density function.
5. Expected value plays a crucial role in determining the best-fit line in linear regression analysis.

Review Questions

• What is the formula for calculating the expected value for a discrete random variable?
• How does expected value assist in making predictions using a regression equation?
• What symbol is commonly used to represent expected value?

Related terms

Random Variable:

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

Probability Distribution:

A function that describes the likelihood of obtaining possible values that a random variable can assume.

Linear Regression: A statistical method for modeling the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.