2Probability Basics

Probability theory is nothing but common sense reduced to calculation.

Pierre Simon Laplace (1749–1827)

In Chapters 2 and 3, we review some fundamental concepts of elementary probability and statistics. If you think you can use these chapters to catch up on all the statistics you forgot since you passed “Introductory Statistics” in your college sophomore year, you are acutely mistaken. What is offered here is an abbreviated reference list of definitions and formulas that have applications to nonparametric statistical theory. Some parametric distributions, useful for models in both parametric and nonparametric procedures, are listed, but the discussion is abridged.

2.1 Helpful Functions

  • Permutations: The number of arrangements of n distinct objects is n factorial equals n left-parenthesis n minus 1 right-parenthesis midline-horizontal-ellipsis left-parenthesis 2 right-parenthesis left-parenthesis 1 right-parenthesis period In R: factorial(n).
  • Combinations: The number of distinct ways of choosing k items from a set of n is
    StartBinomialOrMatrix n Choose k EndBinomialOrMatrix equals StartFraction n factorial Over k factorial left-parenthesis n minus k right-parenthesis factorial EndFraction period

    In R: choose(n,k). Note that all possible ways of choosing items from a set of can be obtained by combn(n,k) ...

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