1. Feb 26, 2008

### laura_a

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...