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Math Help - Marginal Distribution of Rolling 2 Dice

  1. #1
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    Marginal Distribution of Rolling 2 Dice

    I know this is a simple problem but I can't think the correct way to write it out.

    Let X= no. on die 1 and Y= no. on die 2

    f(x,y) = {1/13 for x and y = 1,2,3,4,5,6
    0 otherwise}

    1.Find the marginals of X and Y?

    2. Are X and Y independent?
    I know they are indepented because f(x,y)=g(x)h(y)
    That is true, right?

    I just can't come up with the correct way to solve for the marginals. Will each marginal end up just being 1/6?
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  2. #2
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    Quote Originally Posted by meks08999 View Post
    I know this is a simple problem but I can't think the correct way to write it out.

    Let X= no. on die 1 and Y= no. on die 2

    f(x,y) = {1/13 for x and y = 1,2,3,4,5,6
    0 otherwise}

    1.Find the marginals of X and Y?
    (is that even a probability distribution?)



    The marginal distribution of  X ( a discrete RV) is defined by:

    \displaystyle Pr(X=k)=\sum_i Pr(X=k,Y=y_i)

    2. Are X and Y independent?
    I know they are indepented because f(x,y)=g(x)h(y)
    That is true, right?

    I just can't come up with the correct way to solve for the marginals. Will each marginal end up just being 1/6?
    How can you know this without knowing the marginals?

    f(x,y)=g(x)h(y)

    where  f is the joint probability of  X and  Y ,  g the marginal for  X and  h the marginal for  Y is a necessary and sufficient condition for independence, but you need to show that it is true (or false).


    CB
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  3. #3
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    With how you asked if it was a probability distribution, it what I don't understand. I don't see it as a probability distribution either but we were told to find the marginals of this. So, I'm just confused.

    I know that I need to prove it true, but I have a strong feeling that it will be true.
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