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Stochastics: discrete random variables

  1. Apr 23, 2012 #1
    1. The problem statement, all variables and given/known data
    X1 and X2 are two independent discrete random variables with
    P(X1 = k) = c3-k
    P(X2 = k) = d4-k

    for k in natural numbers and where X1, X2 in natural numbers is almost always valid. 0 is not include in N.

    Find constants c and d.

    2. Relevant equations


    3. The attempt at a solution
    Since I'm joining this class late in the semester I don't know where to begin. Any help is appreciated!!
     
  2. jcsd
  3. Apr 23, 2012 #2

    Curious3141

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    Hint: what must the total probability of all possible events (in the entire sample space) be?

    Another hint: geometric series.
     
  4. Apr 23, 2012 #3
    do you mean sum to infinity?

    [itex]\Sigma^{\infty}_{K=1} c3^{-k} = 1[/itex]

    I see that the series (sn) = c3-k converges.
     
  5. Apr 23, 2012 #4

    Curious3141

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    So what's the sum?
     
  6. Apr 23, 2012 #5
    ya, so in this case (sn) = 3-k converges against 1/2. So c = 2

    thanks!
     
  7. Apr 23, 2012 #6

    Curious3141

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    I would've simply said [itex](c)(\frac{1}{2}) = 1 \Rightarrow c = 2[/itex]. But, yes, you've got the idea. :smile:
     
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