(1.8 hours to learn)
The conditional expectation E[X | Y] is the expectation of X in the conditional distribution P(X | Y).
This concept has the prerequisites:
- expectation and variance
- conditional distributions (Iterated expectation involves taking expectations under conditional distributions.)
- Know the definitions of conditional expectation for both discrete and continuous random variables
- Know and be able to apply the law of iterated expectations
Core resources (read/watch one of the following)
→ Mathematical Statistics and Data Analysis
An undergraduate statistics textbook.
Location: Section 4.4, "Conditional expectation," pages 147-154
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location: Section 4.7, "Conditional expectation," pages 222-228
→ A First Course in Probability
An introductory probability textbook.
Location: Section 7.5, "Conditional expectation," pages 365-382
- Some uses of iterated expectations:
- they justify the use of Monte Carlo estimators
- they are used in the definition of martingales
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