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Probability Mass Function of a Discrete Non-Uniform Distribution

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm having trouble understanding PMF. We are given a number, say, 927189234.

    We need to calculate the PMF of (0, 1, ..., 9) in this distribution.

    2. Relevant equations



    3. The attempt at a solution

    Calculating the probabilities is easy,

    P(9) = 2/9
    P(8) = 1/9
    .
    .
    .
    P(0) = 0/9

    I fail to understand if this is the same as the PMF.

    Any help would be greatly appreciated.
     
  2. jcsd
  3. Oct 23, 2012 #2

    Ray Vickson

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    What do YOU think is meant by the term PMF?

    RGV
     
  4. Oct 23, 2012 #3
    -None-
     
    Last edited: Oct 23, 2012
  5. Oct 23, 2012 #4
    I've understood the PMF by graphing it out,

    So if the X-axis is the (0,1 ..., 9) and the Y-axis are the probabilities, the height of each X-axis value is its PMF. But I don't understand how the Y-axis probabilities are calculated or would they be 0, 1/9, 2/9..., 1.

    I've read that the PMF >= 0 and that the sum of the PMF's of all possible values in a distribution should be equal to 1.
     
  6. Oct 23, 2012 #5

    Ray Vickson

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    Exactly!---although very badly worded. (You don't sum the PMFs; there is just one single PMF and it is a table of the probability values; you are not summing different tables, you are just summing the things in a single table.) So the values of the PMF cannot be 0, 1/9, 2/9, ..., 1 because when you sum these you get something much larger than 1. You seem to be confusing PMF and CDF.

    RGV
     
  7. Oct 23, 2012 #6
    PMF of 9 is 2/9.
     
    Last edited: Oct 23, 2012
  8. Oct 23, 2012 #7

    Ray Vickson

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    Yes.

    RGV
     
  9. Oct 23, 2012 #8
    So the table of PMF is
    {2/9, 2/9, 1/9, 1/9, 1/9, 1/9, 1/9}
    ?

    Thank you.
     
  10. Oct 23, 2012 #9

    Ray Vickson

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    Not quite; you also need to specify the x values (and you need to include zero). I liked your original description P(0) = 0, P(1) = 2/9, etc. much better. That says it all. Or you could make a table with x values in one column (or row) and P(x) values in the other column (or row).

    RGV
     
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