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"It has long been an axiom of mine that the little things are infinitely the most important" (Sherlock Holmes)

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Just a note

  • E() is known as the 'expected' value of .
  • E() is the average value of when you repeatedly calculate it from (equal-sized) random samples of the same population.
    • If you obtain R values of from R samples, the mean value of is Σ/R
    • But if you take every possible (equal-sized) sample of that population R would be infinite. So, to avoid that absurdity, we say Σ/R equals E()

    Notice that, when provides an unbiased estimate of Θ, then E() equals Θ

  • This is the situation with that most well-known statistic, the arithmetic mean. - but it is very seldom true of another popular statistic, the maximum.