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Joint probability density

  1. Apr 23, 2004 #1
    If the values of the joint probability density of Y1 and Y2 are as shown:

    0 1 2 total

    0 1/12 1/6 1/24 35/120
    1 1/4 1/4 1/40 63/120
    2 1/8 1/20 ...... 21/120
    3 1/120 ...... ..... 1/20
    ttl 56/120 56/120 8/120 1

    whew ;-)

    ok Find

    a) P (Y1=0)
    b) P(Y2=1 | Y1=1)
    c P(Y2=1)
    e Check if Y1 and Y2 are independent or dependent
    f Evaluate the correlation coefficient r of y1 and y2

    Thanks so much
     
  2. jcsd
  3. Apr 23, 2004 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Unfortunately, it is not clear from your chart whether Y1 is "across" or "down"!

    Assuming that Y1 can be 0, 1, 2, or 3 (down) and that Y2 can be 0, 1, or 2, (across) then

    P(Y1= 0) is just the sum of the probabilities in the first row (first column if I have Y1, Y2 backwards).

    P(Y2=1 | Y1=1) is the probability in the "1 -1" cell divided by P(Y1= 1).

    P(Y2= 1) is the sum of the probabilities in the second column (second row if I have Y1, Y2 backwards)
     
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