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Math Help - Joint p.m.f

  1. #1
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    Joint p.m.f

    I am studying for a final exam and I am having trouble with getting started with one of my problems. If someone could help explain I would be grateful.

    Let Y be a random variable taking the values -1,0,1 equally likely. Let V be another random variable, independent of Y, and taking the values +1 & 1 with probability 1/2.

    1) Denote by h(y,v) the joint distribution of Y and V. Find h(y,v) (make a table of values)

    2) Let X=YV. Find the p.m.f for X

    3) Let f(x,y) be the joint p.m.f. of X and Y. Find f(x,y)

    4) Are X and Y independent? Reason?

    I have looked in my book and I can't seem to find an example of how to construct the table of values. Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by Cickle View Post
    I am studying for a final exam and I am having trouble with getting started with one of my problems. If someone could help explain I would be grateful.

    Let Y be a random variable taking the values -1,0,1 equally likely. Let V be another random variable, independent of Y, and taking the values +1 & 1 with probability 1/2.

    1) Denote by h(y,v) the joint distribution of Y and V. Find h(y,v) (make a table of values)

    2) Let X=YV. Find the p.m.f for X

    3) Let f(x,y) be the joint p.m.f. of X and Y. Find f(x,y)

    4) Are X and Y independent? Reason?

    I have looked in my book and I can't seem to find an example of how to construct the table of values. Any help would be appreciated.
    Construct a grid with Y along the top and V along the side. The cells contain the probability of things like Pr(Y = 1, V = -1) etc. and you should know how to calculate these probabilities, especially since the events are independent.

    See also advice given here: http://www.mathhelpforum.com/math-he...-function.html
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  3. #3
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    Ok so this is what I am thinking...Is this correct?
    Attached Thumbnails Attached Thumbnails Joint p.m.f-screen-shot-2009-12-05-5.45.24-pm.png  
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  4. #4
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    Quote Originally Posted by Cickle View Post
    Ok so this is what I am thinking...Is this correct?
    Yes.
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  5. #5
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    Thank you so for the second question X=YV find the p.m.f of X

    X would take the values of -1,0,1 correct?

    and from that how would I find the p.m.f for X
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  6. #6
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    Quote Originally Posted by Cickle View Post
    Thank you so for the second question X=YV find the p.m.f of X

    X would take the values of -1,0,1 correct?

    and from that how would I find the p.m.f for X
    Yes.

    Use the table. What cells give you a product of -1? Add up the probabilities. etc.
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  7. #7
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    I guess I am still a little confused so if X=-1 then the it would be 1/6 +1/6 if X=0 it would be 1/6 + 1/6 and if X=1 it would be 1/6?
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  8. #8
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    Quote Originally Posted by Cickle View Post
    I guess I am still a little confused so

    if X=-1 then the it would be 1/6 +1/6 Mr F says: Yes.

    if X=0 it would be 1/6 + 1/6 Mr F says: Yes.

    and if X=1 it would be 1/6? Mr F says: No.
    Does 1/3 + 1/3 + 1/6 = 1? So clearly one of these three is wrong ....

    Note that 1 = (1)(1) and (-1)(-1).
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  9. #9
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    Sorry I meant 1/6 + 1/6 for the last one too. So how would I write that for it to make sense? f(x)=2/6 for x=-1,0,1 ?

    and then for the third question the joint p.m.f. f(x,y)=1/3 * 2/6=1/9 for x=-1,0,1 and y=-1,0,1

    and the the fourth they would be independent because f(x,y)=f(x)f(y)

    And thank you for your patience I am just trying to make sure that I fully grasp this for my final.
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