Expectation and Linearity of Expectation

Learn expectation and linearity of expectation.

24 min read
Intermediate

Introduction

Learning Objectives:

  • Calculate expectations
  • Apply linearity of expectation
  • Use indicator variables

Expectation

E[X]=sumxxcdotP(X=x)quadext(discrete)E[X] = sum_x x cdot P(X = x) quad ext{(discrete)} E[X]=int−inftyinftyxcdotfX(x),dxquadext(continuous)E[X] = int_{-infty}^{infty} x cdot f_X(x) , dx quad ext{(continuous)}

Linearity: E[aX+bY]=aE[X]+bE[Y]E[aX + bY] = aE[X] + bE[Y] (no independence needed!)

Key Concepts

This lesson covers fundamental concepts in probability theory.

Key Takeaways

Master these concepts for advanced probability applications.

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Combinatorics and Probability: From Counting to Inference

Master the mathematical foundations of counting, probability, and randomness. This comprehensive course bridges pure combinatorics with computational probability, covering everything from basic counting principles to advanced probabilistic methods, limit theorems, and real-world applications in algorithms, finance, and data science.