Variance, Standard Deviation, and Covariance

Learn variance, standard deviation, and covariance.

23 min read
Intermediate

Introduction

Learning Objectives:

  • Calculate variance and standard deviation
  • Understand covariance and correlation
  • Use variance properties

Variance

extVar(X)=E[(X−E[X])2]=E[X2]−(E[X])2 ext{Var}(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2

Standard deviation: sigmaX=sqrtextVar(X)sigma_X = sqrt{ ext{Var}(X)}

Covariance

extCov(X,Y)=E[(X−E[X])(Y−E[Y])]=E[XY]−E[X]E[Y] ext{Cov}(X,Y) = E[(X - E[X])(Y - E[Y])] = E[XY] - E[X]E[Y]

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.