convergence in probability and strong convergence in the discrete case

[phychoflip29]

Show that if you have convergence in probability, then you also have strong convergence in the discrete case. I know that the discrete case means that the sum as i = 0 to n, P(Xi=xi) = 1. I don't know how to start it and continue. Thank you so much for your help.

[Dason]

Hi! We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.

It's also not clear to me what you mean by the terms you're throwing around. Part of that might be the pseudo-math syntax you're trying to use. You can read about how to make math easier to read here: http://www.talkstats.com/showthread....-use-Math-tags

[Dragan]

I suspect that what the OP might be referring to is the Weak (versus Strong) Law of Large Numbers - where the mode of convergence is strengthened from convergence in probability (Weak Law) to almost certain convergence (Strong Law).

[phychoflip29]

Thanks for the responses and thanks for the guidelines! I also read my text that my professor gave me and tried to do it, and i looked on a search engion trying to search for discreet probability and i got =. I thought about using the proof of since that is the only proof i the text. And there is no proof for convergence in probability. But then I thought whats the point of trying to do the proof for strong convergence if i want to prove strong convergence by convergence in probability. (strongly = almost surely)

Maybe it would be easier if i said,

[BGM]

http://en.wikipedia.org/wiki/Proofs_..._discrete_case

Wikipedia just gives a counter-example to disprove your claim.