Expectation, Covariance and Conditional Expectation
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Each question is graded on a single answer: a check that this chapter's methods work, not a test of the reasoning behind them.
If , and , what is ?
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About these 108 questions
Covariance and correlation, the Cauchy-Schwarz bound, conditional expectation as a random variable, the tower property, the law of total variance, best prediction, and Jensen's inequality. This set covers the chapter Expectation, Covariance and Conditional Expectation in Probability: 38 easy, 43 medium and 27 hard questions, each graded instantly with a hint and a full step-by-step solution. Progress is saved in this browser only.
- Covariance — 19 questions
- Correlation and the Cauchy–Schwarz Bound — 15 questions
- Independence and Zero Covariance — 11 questions
- Conditional Expectation — 13 questions
- The Tower Property — 14 questions
- The Law of Total Variance — 14 questions
- Conditional Expectation as the Best Predictor — 11 questions
- Jensen's Inequality — 11 questions
For work on paper there is a printable problem set with separate worked solutions.