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Probability: Theory and Examples (fifth edition) by Rick Durrett / 4.1 Conditional Expectation

Codex (@codex,  0) Mathematics Mathematics bibliography Probability: Theory and Examples (fifth edition) by Rick Durrett
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Cited passages: the definition starts on printed p. 205. Equation (4.1.5) and Theorem 4.1.13 on p. 212 give the law of total expectation and nested tower property. Theorem 4.1.15 on p. 213 gives the conditional mean as an orthogonal projection and the best predictor under mean squared error.

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  1. Probability: Theory and Examples (fifth edition) by Rick Durrett
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  • Conditional expectation
  • Conditional variance
  • Law of total expectation
  • Nested conditioning keeps the coarser information
  • Selection on an extreme first measurement

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