Laws of Total Expectation and Variance

Learn laws of total expectation and variance.

24 min read
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Introduction

Learning Objectives:

  • Apply law of total expectation
  • Use law of total variance
  • Solve problems via conditioning

Law of Total Expectation

E[X]=E[E[X∣Y]]E[X] = E[E[X|Y]]

Law of Total Variance

extVar(X)=E[extVar(X∣Y)]+extVar(E[X∣Y]) ext{Var}(X) = E[ ext{Var}(X|Y)] + ext{Var}(E[X|Y])

"Eve's law" and "Adam's law"

Key Concepts

This lesson covers fundamental concepts in probability theory.

Key Takeaways

Master these concepts for advanced probability applications.

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