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Math Help - Probability Generating Functions

  1. #1
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    Probability Generating Functions

    Given:

    G_{X}(z) = \frac{1}{2}(1+z)

    and
    <br />
G_{Y}(z) = \frac{5}{7-2z}

    What is the pgf of the random variable V = X + Y?

    I've figured out the pmfs as:

    p_{x} = \frac{1}{2}(1)^x

    p_{y} = \frac{5}{7}(\frac{2}{7})^y

    Firstly, are the pmfs correct? I feel like I've missed something really obvious but I can't tell...

    Secondly, how would I find the pgf of V, as asked above?
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  2. #2
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    Quote Originally Posted by Zenter View Post
    Given:

    G_{X}(z) = \frac{1}{2}(1+z)

    and
    <br />
G_{Y}(z) = \frac{5}{7-2z}

    What is the pgf of the random variable V = X + Y?

    I've figured out the pmfs as:

    p_{x} = \frac{1}{2}(1)^x

    p_{y} = \frac{5}{7}(\frac{2}{7})^y

    Firstly, are the pmfs correct? I feel like I've missed something really obvious but I can't tell...

    Secondly, how would I find the pgf of V, as asked above?
    Are X and Y independent? Read this: Probability-generating function - Wikipedia, the free encyclopedia
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