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Averages in involving multiple variables

We'll consider both continuous and discrete variables. They're quite similar once you get the hang of it, but because both have important applications we'll consider both.

• Contents
• Probability
  • Why Study Probability?
  • What is Probability?
    • Darwin awards
    • Not so fast, Charles
  • Calculation of Probability
    • Independence
    • Venn Diagrams
    • Bayes's Theorem
      • Cracking a lock
      • Back to Independence
    • Problems
    • Counting possibilities
      • Question
      • Question
    • Return to New York
      • Questions
    • Binomial Expansion
    • Binomial Distribution
      • Problems
    • Plotting the distro
    • Sharpness as N gets bigger
  • Continuous distributions
    • Problem
    • Infinitesimals in probability
    • Problem
  • Averaging
    • Gambling doesn't pay, sometimes
    • There are many ways to skin a guanabana
    • Averages of continuous variables
    • Properties of averages
    • Problems
    • Averages in involving multiple variables
      • Averages in involving multiple discrete variables
      • Averages in involving multiple continuous variables
      • Averages for independent variables
      • Problem
      • Average of a Binomial Distro
    • Variance: just how fat is your distribution?
      • *Variance of binomial distro
      • Problems
  • Gaussians are quite normal
    • Here there and everywhere
      • Problem
      • Was this a freak accident?
      • Variance of N variables
  • Random Walks
  • Correlations
    • Correlation vs. Causation
    • Linear Regression
  
  
• Statistics
  • Introduction
  • Simple Example
  • Unbiased estimates
  • Hypothesis testing
  • But what if I goofed?
  • Goofing up for fame and fortune
  • Forming a statistic
  • The shape of the distribution
    • Variance of mean differences
    • There's no such thing as a brontosaurus
  • How to do the t-test
  • Example
    • t-test data example
  • Can you beat Wall Street?
    • What are stocks?
    • Stock Trading: a market minute on NASDAQ
    • Bob's uncanny stock investment advice
      • Signal to noise
    • How random?
    • Deceptive Correlations
  • Stocks and Random Walks
    • Random Walks and Volatility
      • Volatility example
  • Stock beta calculation
  
  
• About this document ...