Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proving if a function is a valid probability distribution

  1. Oct 24, 2007 #1
    Hi,

    Given the function:

    [tex]P_{k} = \frac{20}{5^{k}}[/tex] for [tex]k \geq 2[/tex]

    How would you prove that P is a probability distribution? I would think that you prove that P is bounded by 0 and 1 (i.e., [tex]0 \leq \Sigma P_{k} \geq 1[/tex])

    And I guess the leading question is how you would prove that a function is not a probability distribution?
     
  2. jcsd
  3. Oct 24, 2007 #2

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    You also need that
    [tex]\sum_{k=2}^\infty\frac{20}{5^k}=1[/tex]
     
  4. Oct 24, 2007 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You would prove that a function is NOT a valid probability distribution by showing that at least one of those conditions is not true. That is, that
    1) Pk < 0 for some k or
    2) Pk > 1 for some k or
    3) [tex]\sum_{k=2}^\infty\frac{20}{5^k}\ne 1[/tex]
     
  5. Nov 8, 2007 #4
    Cheers
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Proving if a function is a valid probability distribution
Loading...