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A EASY QUESTION FOR probability probability A easy question for probability

  1. Aug 7, 2012 #1
    Let X; Y be two random variables with the following joint distribution(in the attachment):



    (a) Compute p(X) and p(Y )
    (b) Compute p(X|Y = 1)
    (c) compute p(Y = 1|X = 1) using (a) and (b)
    (d) Are X and Y statistically independent? Show all your working.




    This is my answer, but I don't know whether it's correct
    (a) joint probabilities:
    p(X=1)= 0+1/8=1/8
    p(X=2)= 3/4+1/8=7/8
    so p(X)= 1/8+7/8=1
    p(Y=1)= 0+3/4=3/4
    p(Y=2)=1/8+1/8=1/4
    so p(Y)=3/4+1/4=1
    just like Millennial said, I also don't understand this question, because I think it doesn't make any sense.

    (b) p(Y=1,X) = p(Y=1)p(X|Y=1)
    so p(X|Y=1) = p(Y=1, X)/p(Y=1) =?/(3/4)
    here I have a question, I don't know how to compute p(Y=1,X), and btw does p(Y=1,X) = p(X, Y=1)?

    (c) because I can't actually compute (b), so just leave it behind for now.

    (d) because p(X=1,Y=1) = 0 and it doesn't equal to p(X=1)p(Y=1) = 1/8,so they are not statistically independent.
     

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    Last edited: Aug 7, 2012
  2. jcsd
  3. Aug 7, 2012 #2
    I didn't understand anything. Are X and Y, 1 or 2? Or is 1 the happening probability of Y and X?
     
  4. Aug 7, 2012 #3
    You misunderstood the assignment; it's you who are supposed to do it, not us. Maybe show us what you got so far and we might be able to help.
     
  5. Aug 7, 2012 #4

    NascentOxygen

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    Staff: Mentor

    The table may be clearer if the label p(X,Y) didn't appear on the figure, but instead were printed underneath the figure as a caption.
     
  6. Aug 7, 2012 #5

    Simon Bridge

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    fhjop1: welcome to PF.
    clamtrox is correct - since you say the question is "easy", what's the problem?
     
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