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Math Help - another joint distribution question

  1. #1
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    another joint distribution question

    P(X=x,Y=y)=1/8 for x =3,5 and y=1,2,4,7
    P(X=x,Y=y)=0 otherwise
    a) What is Fxy(x,y) for all x,y in R
    b) What is pxy(x,y) for all x,y in R
    c) What is px(x) for all x in R
    d) What is py(y) for all y in R
    e) What is the the marginal cdf Fx(x) for all x in R
    f) What is the the marginal cdf Fy(y) for all y in R

    My attempt
    ----------
    a)

    Fxy(x,y) =
    y<1 1<=y<2 2<=y<4 4<=y<7 y<=7
    x<3 0 0 0 0 0
    3<=x<5 0 1/8 2/8 4/8 6/8
    x<=5 0 2/8 4/8 6/8 8/8

    1 if otherwise

    b)

    Pxy(X=x,Y=y)= 1/8 if x is 3,5 and y is 1,2,4,7
    0 otherwise

    c)
    Last edited by Sneaky; October 17th 2010 at 05:05 PM.
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  2. #2
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    Quote Originally Posted by Sneaky View Post
    P(X=x,Y=y)=1/8 for x =3,5 and y=1,2,4,7
    P(X=x,Y=y)=0 otherwise
    a) What is Fxy(x,y) for all x,y in R
    b) What is pxy(x,y) for all x,y in R
    c) What is px(x) for all x in R
    d) What is py(y) for all y in R
    e) What is the the marginal cdf Fx(x) for all x in R
    f) What is the the marginal cdf Fy(y) for all y in R

    My attempt
    ----------
    a)

    Fxy(x,y) =
    y<1 1<=y<2 2<=y<4 4<=y<7 y<=7
    x<3 0 0 0 0 0
    3<=x<5 0 1/8 2/8 4/8 6/8
    x<=5 0 2/8 4/8 6/8 8/8

    1 if otherwise

    b)

    Pxy(X=x,Y=y)= 1/8 if x is 3,5 and y is 1,2,4,7
    0 otherwise

    c)
    X and Y are both discrete distributions. I suggest you format your answers using a table or grid.
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  3. #3
    Senior Member
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    here is a clear pic


    is what I did for a and b right?


    for e)
    Fx(x)=
    0 if x<3
    1/2 if 3<=x<5
    2/2 if x<=5
    1 otherwise
    for f)
    Fy(y)=
    0 if y<1
    1/4 if 1<=y<2
    2/4 if 2<=y<4
    3/4 if 4<=y<7
    4/4 if y<=7
    1 otherwise
    Last edited by Sneaky; October 17th 2010 at 06:14 PM.
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