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Math Help - Prob distribution of a throw of the die

  1. #1
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    Prob distribution of a throw of the die

    The probability distribution is {1 \over 6} for k=1,2,3,4,5,6.

    But what is its generating function?
    Can anyone explain why it is { {s+s^2+s^3+s^4+s^5+s^6} \over {6}}
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  2. #2
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    Got it.
    We shold not be fixated in the form of s but rather its coefficients.

    To generate the coefficients of 1,1,1,1,1,1, the generating function is:
    {{s (1-s^6)} \over {1-s} } = s+s^2+s^3+s^4+s^5+s^6

    Thanks for reading.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by chopet View Post
    The probability distribution is {1 \over 6} for k=1,2,3,4,5,6.

    But what is its generating function?
    Can anyone explain why it is { {s+s^2+s^3+s^4+s^5+s^6} \over {6}}
    It is this by definition of the probability generating function of the distribution.

    Why this is a useful definition is another mater, and the answer to that is
    its usefully properties (you should also note that it encapsulates all the
    information in the pmf). Some of the properties that are of use can be found
    here.

    You should note that this is a z-transform of the pmf, which is the
    discrete analogue of the Laplace transform, which of course with a bit
    of jiggery-pokery gives the moment generating function for a continuous
    distribution.

    RonL
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