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Unknown in discrete variable problem

  1. Mar 6, 2005 #1
    Let X be a random variable with probability function:
    [itex]fx(x) = c/x!, x = 0, 1, 2, ...[/itex]

    Find c.

    By first guess was to form the sum:
    [itex]\sum_{i=0}^{x} c/i! = 1[/itex]
    But I have no idea if that's the right approach or how to proceed.
     
  2. jcsd
  3. Mar 6, 2005 #2
    Probably you have to normalize the probability function, in other words the total probability should be 1:

    [tex] \sum_{x=0}^{\infty} f(x) = 1 [/tex]

    This is easy because:

    [tex] \sum_{x=0}^{\infty} \frac{1}{x!} = e [/tex]
     
  4. Mar 6, 2005 #3
    ahhh!
    stupid me wasn't aware of that result, thanks heaps for that.




    thanks, [itex] c = 1/e[/itex] for anyone whos interested. I was able to complete the other problems relating to this question.

    however I have one small problem, in my studies i've learnt "a random variable X will be defined to be discrete if the range of X is countable" - introduction to theory of statistics (mood). but since the values of X was unbounded in the question (X = 0, 1, 2, ...) i.e: [itex]Z+[/itex] that is uncountable. ?
     
    Last edited: Mar 6, 2005
  5. Mar 8, 2005 #4

    honestrosewater

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    Gold Member

    Does countable mean finite or countably infinite? It almost surely means countably infinite. The nonnegative integers are easily seen to be countable:
    {1, 2, 3, ...}
    {0, 1, 2, ...}
    I can't read your original question, so if you meant something else by "unbounded", sorry, but the nonnegative integers are bounded below by 0.
     
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