Expected Value

The expected value of a discrete random variable is the sum of the product of the probability of each event by the value of that event.

Expected Value Formula

The expected value of a random variable, X, is denoted by µ or E(X).


Variance of a Discrete Random Variable

Variance of a Discrete Random Variable

Standard Deviation of a Discrete Random Variable

Standard Deviation of a Discrete Random Variable

Example

Calculate the expected value, variance, and standard deviation of the probability distribution for the possible outcomes that can be obtained by throwing a die.

 x p i x · p i x 2 · pi
1 p p p
2 p p p
3 p p x 2 ·pi
4 p p x 2 ·pi
5 p p x 2 ·pi
6 p 1 6
             sumatoria sumatoria

Expected Value Exercise

Expected Value Operations

Expected Value Solution