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Math Help - Joint Probability mass problem

  1. #1
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    Joint Probability mass problem

    Hello All,

    This is my first time visitnig math helop forum and I was wondering if anyone could help me with a HW problem. I have posted it below. Thanks a lot:



    1. The problem statement, all variables and given/known data

    X and Y are random variables and have the following joint probability mass function

    q(x,y)=1/p^2 for x=1,2,....p and y=1,2,....p

    are x and y independent?


    2. The attempt at a solution

    What I want to do is find the marginals for x and y and then see if q(1,1) is equivalent to qx(1) times qy(1)

    I know the marginal for x is the summation from y=1 to p of 1/p^2. Y is the same except switch to x for the summation. I just don't know how to get the summation. Can anyone help with this?

    Secondly, can P(1,2) even exists? Don't the x and y values have to be the same since p(x,y) is 1/p^2 and if x and y are different, what value would you use for p?

    I'm completely lost and I would appreciate all help. Thanks.
    I would appreciate any help with this problem. Thank You.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jackroberts4 View Post
    Hello All,

    This is my first time visitnig math helop forum and I was wondering if anyone could help me with a HW problem. I have posted it below. Thanks a lot:



    1. The problem statement, all variables and given/known data

    X and Y are random variables and have the following joint probability mass function

    q(x,y)=1/p^2 for x=1,2,....p and y=1,2,....p

    are x and y independent?


    2. The attempt at a solution

    What I want to do is find the marginals for x and y and then see if q(1,1) is equivalent to qx(1) times qy(1)

    I know the marginal for x is the summation from y=1 to p of 1/p^2. Y is the same except switch to x for the summation. I just don't know how to get the summation. Can anyone help with this?

    Secondly, can P(1,2) even exists? Don't the x and y values have to be the same since p(x,y) is 1/p^2 and if x and y are different, what value would you use for p?

    I'm completely lost and I would appreciate all help. Thanks.
    I would appreciate any help with this problem. Thank You.
    The marginal distribution of $$x is:

    \displaystyle P_X(x)=\sum_{i=1}^p \frac{1}{p^2}=\frac{1}{p},\ \ x=1,..,p

    similarly the marginal distribution of $$y is:

    \displaystyle P_Y(y)=\sum_{i=1}^p \frac{1}{p^2}=\frac{1}{p},\ \ y=1,..,p

    We now observe that:

    q(x,y)=P_X(x)P_Y(y)

    and so $$X and $$Y are independent.

    CB
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