Six Sigma and Beyond: Statistics and Probability, Volume III

  1. Problem: The frequency or number of observations within a cell , f k , depends upon the total sample size , n.

    In the example, n = 20; however, if n is increased to 100, then values of frequency, f k , may change.

  2. Solution: Normalize frequency by the total sample size n.

    Defines the probability density function (pdf) of the grouped range values X k :

  3. Assumes: Each observed sample is independent of others and represents equally likely events.

    Example Problem: n = 20

    Cell, RV X k

    Frequency f k

    Probability f(X k ) = f k /n

    2

    8

    0.40

    3

    5

    0.25

    4

    4

    0.20

    5

    2

    0.10

    6

    1

    0.05

     

    20

    1.00

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