CONCEPT INDEX

Probability & Statistics

Below is a summary of the content areas covered by modules about Probability and Statistics. Many of these concepts have modules that illustrate the concepts visually, and allow user input. Most modules were written as part of the Project Links NSF Grant. A few are from other sources, but are appropriate to this topic.

Essentials of Probability

• Probability on a Sample Space
  • Basic Operations on Events
  • Probability on Events
  • Other Properties of Events
• Conditional Probability
• Bayes Formula
• Total Probability Theorem
• Independence
• Random Variables
  • Random Variable as a Measurement
  • Probability Mass Function (PMF) for a Discrete Random Variable
  • Cumulative Distribution Function (CDF)
  • Probability Density Function (pdf) for Continuous Random Variables
  • Properties of Continuous Random Variables
  • Expectation
    • Expectation of a Discrete Random Variable
    • Expectation of a Continuous Random Variable
    • Moments about the Origin
    • Moments about the Mean
    • Mean
    • Variance
  • Important Discrete Random Variables
    • Bernoulli Random Variable
    • Binomial Random Variable
    • Geometric Random Variable
    • Poisson Random Variable
  • Important Continuous Random Variables
    • Uniform Distribution
    • Normal/Gaussian Distribution
      • Normal/Gaussian CDF & Tables
      • Using Normal/Gaussian pdf's and CDFs to integrate definite integrals of the form e^-(ax2+bx+c)
    • Exponential Distribution
    • Gamma Distribution
    • Chi-Square Distribution
    • Erlang Distribution
    • Beta Distribution
    • Cauchy Distribution
    • Laplacian Random Variable
    • Rayleigh Random Variable
    • Lognormal Random Variable
  • Relationships between different types of Random Variables
    • Geometric and Exponential Distributions
    • Poisson and Exponential Distributions
    • Poisson and Binomial Distributions
    • Gamma (Erlang) and Poisson Distributions
    • Gaussian & Chi-Square Random Variables
  • Pairs of Random Variables
    • Jointly Gaussian Random Variables
  • Mulitple Dimensional Random Variables
• Central Limit Theorem (CLT) Applet (guest module)

Statistics

• Mean, Median & Mode
• Samples of a Random Variable
• Histograms
  • Histogram Applet (guest module)

Application Fields

• Communication Networks
  • Computer Networks Notes

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