Topics: Probability - Expected Value


Let be a random variable and let be a function such that is also a random variable.

If we wanted to calculate , the expected value of , we would have to first find (its density function). There is, however, a simpler way to calculate it, called the law of the unconscious statistician.

Discrete Case

If is a discrete random variable, then:

Continuous Case

If is an absolutely continuous random variable, then: