That's exactly it. I was getting a little lazy with the notation and wasn't sure how deep into the rabbits hole you've gone. So yes that is it and you should see that the X(\omega) cancels and you're just left with 1/i in there which you can make arbitrarily small so we have convergence in probability.
Really convergence in probability is mostly used for convergence to constants though and is then used along with Slutsky's theorem to do something more interesting with convergence in distribution.
Last edited by Dason
on Sat Apr 28, 2012 4:29 pm UTC, edited 1 time in total.
double epsilon = -.0000001;