AI engineering glossary · Probability
What is law of total expectation?
Law of total expectation: The overall expected value of a variable equals the average of its conditional expected values, weighted by the probabilities of the conditions: E[X] = sum of E[X | B] x P(B). It splits a hard average into easier cases.
Law of total expectation: an example
If mobile users spend Rs 300 on average (60% of users) and web users Rs 500 (40%), overall average is 0.6 x 300 + 0.4 x 500 = Rs 380.
Related terms
More Probability terms
- Law of total probability
- Likelihood
- Linearity of expectation
- Marginal distribution
- Marginal probability
- Markov chain
- Markov chain Monte Carlo
- Markov property
Where you learn it
Law of total expectation is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.