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Math Help - need help pmf

  1. #1
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    Question need help pmf

    1. The joint probability distribution of two discrete random variables X and Y are given by the following joint probability mass function:

    P( X=x, Y=y ) = k | x y |, x = 1, 2, 3 ; y = 2, 4, 5
    = 0, otherwise.

    (a) Find the constant k
    (b) Find the marginal distributions of X and Y
    (c) Calculate the correlation coefficient between X and Y
    (d) Are X and Y Independent ?
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  2. #2
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    Quote Originally Posted by amul28 View Post
    1. The joint probability distribution of two discrete random variables X and Y are given by the following joint probability mass function:
    P( X=x, Y=y ) = k | x y |, x = 1, 2, 3 ; y = 2, 4, 5
    = 0, otherwise.
    (a) Find the constant k
    Let A = \left\{ {1,2,3} \right\} \times \left\{ {2,4,5} \right\}~then ~k = \left( {\sum\limits_{(x,y) \in A} {\left| {x - y} \right|} } \right)^{ - 1} .
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  3. #3
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    so is it equal to 1/6 ?
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    Quote Originally Posted by amul28 View Post
    so is it equal to 1/6 ?
    There are nine pairs in A.
    You have to sum nine numbers to get k.
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  5. #5
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    Quote Originally Posted by Plato View Post
    There are nine pairs in A.
    You have to sum nine numbers to get k.

    so it is 1/17
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  6. #6
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    Quote Originally Posted by amul28 View Post
    so it is 1/17
    Yes it is.
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