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Math Help - Generating Functions help

  1. #1
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    Generating Functions help

    Hey there everyone, I need some help with this math problem, hoping to get some help on this topic.


    Use generating functions to find the number of solutions in integers to the equation a+b+c=30 where each variable is at least 3 and at most 7.

    Please explain to me step by step on how to do this so I can understand it better thanks.
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  2. #2
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    Re: Generating Functions help

    Hey gfbrd.

    Given your constraints you will never get a solution since your maximum value will be 7+7+7=21 and your minimum will be 3+3+3=9. Did you mean to say something else?

    Edit: Can't add up properly.
    Last edited by chiro; October 26th 2012 at 10:53 PM.
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  3. #3
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    Re: Generating Functions help

    Nope that is how the question is, so there should be some kind of answer
    oh and 7+7+7=21 not 24
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  4. #4
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    Re: Generating Functions help

    Thanks for pointing out the error.

    Well it sounds like what they want you to do is have two independent random variables with 3 to 7 and then have another random variable which is 30 minus the sum of those two.

    The sum of two random variables' distribution can be found with a PGF and this will be based on two uniform distributions of 5 values with same probability for 3 to 7 inclusive.

    Then the other variable will be 30 - (X+Y) but 30 is just a special case of a distribution where you have Z - W where Z has a probability density function of P(Z=30) = 1 and the distribution of -W just reflects the distribution around the y-axis.

    So can you calculate for a start the PGF for the sum of two uniform random variables (discrete uniform) with values going from 3 to 7 inclusive.
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  5. #5
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    Re: Generating Functions help

    lol sorry im not understanding this
    if you dont mind i hope you can make it more simple for me to understand hahaha sorry im slow at this kind of stuff
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  6. #6
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    Re: Generating Functions help

    Let X = Uniform(3,7) and Y = Uniform(3,7) as well. Use the PGF formula to find the probability generating function for X+Y if X,Y are independent.
    Thanks from gfbrd
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  7. #7
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    Re: Generating Functions help

    oh alright I get it now thanks for your help
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