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Math Help - discrete random variable

  1. #1
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    discrete random variable

    Statement of the problem:
    Discrete random variable x is described by the PDF:
    px(xo) = (5-xo)/12 if xo = 0,1,2
    px(xo) = 0 otherwise

    let d1, d2, d3,...dN represent N successive independent experimental values of random variable x.

    Determine the probability that d1>d2
    Determine the probability that d1+d2+...dN <= 1.0
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rbenito View Post
    Statement of the problem:
    Discrete random variable x is described by the PDF:
    px(xo) = (5-xo)/12 if xo = 0,1,2
    px(xo) = 0 otherwise

    let d1, d2, d3,...dN represent N successive independent experimental values of random variable x.

    Determine the probability that d1>d2
    Determine the probability that d1+d2+...dN <= 1.0
    p(d1>d2)=p(d2>d1)

    and

    1=p(d1>d2)+p(d1=d2)+p(d2>d1)= 2p(d1>d2)+p(d1=d2)

    so:

    p(d1>d2)=[1-p(d1=d2)]/2

    p(d1=d2)=p(d1=0)p(d2=0) + p(d1=1)p(d2=1) + p(d1=2)p(d2=2)

    ............ =p(d1=0)^2+p(d1=1)^2+p(d1=2)^2

    RonL
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