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Interpretation of random variable

  1. Sep 22, 2009 #1
    1. The problem statement, all variables and given/known data
    The probability mass function of a random variable X is:
    P(X=k) = (r+k-1 C r-1)pr(1-p)k
    Give an interpretation of X.

    2. Relevant equations



    3. The attempt at a solution
    The PMF looks like the setup for a binomial random variable. The first combination looks like you are arranging r-1 successes in r+k-1 slots. And the pr seems like it is giving the probability of r successes occurring. But I don't see what X as a whole is standing for.
     
  2. jcsd
  3. Sep 23, 2009 #2

    lanedance

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    Homework Helper

    i think you;re almost there, so i assume you mean
    [tex] P(X=k) = C_{r-1}^{r+k-1}p^r(1-p)^k [/tex]

    can re-write this as
    [tex] P(X=k) = p.C_{(r-1)}^{k+(r-1)}p^{r-1}(1-p)^{k} [/tex]

    which as you say comparing with the binomial distribution is for n trials, m success, and probabilty of success of p

    can re-write this as
    [tex] P(M=m) = p.C_{m}^{n}p^{n-m}(1-p)^{m} [/tex]

    so your distribution is effectively p (the probabilty of a single success) times the probability of r-1 successes out of r-1+k trials (with probability of success p).

    any ideas for an interpretation of this as a total entity?
     
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