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Math Help - Trinomial Distribution

  1. #1
    Rhymes with Orange Chris L T521's Avatar
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    Trinomial Distribution

    I've been struggling with this particular distribution. I'm told that X and Y have a trinomial distribution with parameters n=3, p_1=\tfrac{1}{6} and p_2=\tfrac{1}{2}

    I know that the joint pmf is f(x,y)=\frac{6}{x!y!(3-x-y)!}\left(\tfrac{1}{6}\right)^x\left(\tfrac{1}{2}\  right)^y\left(\tfrac{1}{3}\right)^{3-x-y}

    I'm asked to find various things, such as

    E(X)

    E(Y)

    \text{Var}(X)

    \text{Var}(Y)

    \text{Cov}(X,Y)

    and \rho

    I don't want anyone to solve all of these.

    However, if someone can show me how to find the expected value of either x or y, I would be able to figure out the rest.

    I have an inkling that E(X)=\mu_x=\sum_{x} xf_X(x), but how would I find the marginal of X???

    I'd appreciate any input!!

    --Chris
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
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    nvm....I overcomplicated this. I figured it out.

    --Chris
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