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Probability (probability mass function,pmf)

  1. Dec 15, 2009 #1
    If X has the probability mass function f(x) = k / x! (x=0,1,2,...),
    what is the value of k?
     
  2. jcsd
  3. Dec 15, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    I think you mean "probability density function".

    The total probability must be 1.
    [itex]\sum_{x=0}^\infty k/x!= k\sum_{x=0}^\infty 1/x!= 1[/itex]

    Do you know what that sum is?
     
  4. Dec 15, 2009 #3
    i dont know.. is it infinity?
     
  5. Dec 15, 2009 #4

    statdad

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    For discrete distributions these are usually called mass functions - density is reserved for continuous distributions.

    naspek, HallsofIvy is asking whether you can identify what the sum

    [tex]
    \sum_{x=0}^\infty \frac 1 {x!}
    [/tex]

    equals? This problem should remind you of a commonly used distribution.
     
  6. Dec 15, 2009 #5

    HallsofIvy

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    You probably have not taken calculus yet, but if you had you would have learned that
    [tex]e^x= \sum_{n=0}^\infty \frac{x^n}{n!}[/tex].

    Do you know what an "exponential probability distribution" is?
     
    Last edited: Dec 16, 2009
  7. Dec 15, 2009 #6
    ok.. now i understand already... thanks guys!! =)
     
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