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Roll 2 fair dice, find pdf and cdf

  1. Nov 30, 2011 #1
    Hi guys. I have a test tomorrow and I am trying to work out the problems on the review sheet, but I can't figure out this one dealing with pdf and cdf.

    Roll 2 fair dice and call each outcome (i,j) where i,j = 1,2,...6.
    Define: X= {i+j if i+j ≤ 6 ; abs.value(i-j) otherwise}

    A) Find and draw the pdf.
    B) Find and draw the cdf.



    The professor sent us the solutions. I just can't figure out how he got it. The solution he sent was:

    a)
    f(x)= { 3/36 if x=o; 5/36 if x=2 or 4 or 6; 6/36 if x=1 or 3 or 5}

    b) f(x)= {0 if x<0; 3/36 if 0≤x<1; 9/36 if 1≤x<2; 14/36 if 2≤x<3; 20/36 if 3≤x<4; 25/36 if 4≤x<5; 31/36 if 5≤x<6; 1 if x≥6}

    Could someone please help me understand the steps to take to get this answer?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 1, 2011 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    First find the probabilities of all the individual pairs (i,j). For each pair (i,j), figure out what x must be. Of course, the same x might be obtained for several different pairs (i,j), so you need to be careful. That's it; that's all there is to it.

    RGV
     
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