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Can someone Please help me understand what a distribution of probability function is

  1. Feb 26, 2008 #1
    1. The problem statement, all variables and given/known data
    I have the following question

    p(x) = log_10(1 + 1/x) for x = 1,2,3, ... 9 (otherwise p(x)=0)

    So firstly I had to prove that p(x) is a probability function, which I have done so (by proving the sum of all the values =1)
    anyway the second thing I have to do is determine an expression for the corresponding distribution function. How exactly do I do this? The information on wiki is confusing and the text book doesn't seem to cover it? Can anyone help?

    2. Relevant equations

    3. The attempt at a solution

    I've read 2 text books and the internet and I can't find an exact method or style of answer, but I know it has to have inequalities in it and I have done some working out plugging in each value and getting an answer, but I am unable to write it out in the format that the text book has... that is would be something like

    P_x(x) = { 0 for x <1
    ... etc... but if I wrote something like =1 for x<=9 that isn't exactly true because if x was 8.5 then it wouldn't equal one.... this is what I was just working on when I realised I must have the wrong idea... the question asks me to write an expression for the distribution function.... is there a simple way I can just write a general?? Do I need to interal because I have worked that out just in case...

    Thanks for any help you can give me..
  2. jcsd
  3. Feb 26, 2008 #2
    What you're working with here is a discrete probability function, as you probably know. For each x you get the probability for that outcome. The random variable presumably denoted X has for example a chance log10(1 + 1/1) = log10(2) of being 1, and so on for the other defined values of x.

    A distribution function, on the other hand, doesn't give you the probability that X is equal to x, but the probability that the outcome of X is less than or equal, to the given x. In this case, it's just the sum of all p(y) where 1 <= y <= x.
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