The use of "for" and "and" is correct but should be the number(s) that E[I] takes under the conditions described.
I am not sure about the notation of a case by case problem. This is my solution:
Is that the correct way to display a case by case analysis? Specifically I would like to know, if there is a more elegant way than my solution. Is the phrasing "for" and "and" the way to do it? What about "otherwise"? I have only little experience in mathematical notation and therefore I'd be glad about comments about my "mathematical style"
Thanks for your help. All I want to say is that E[I] will be less than one if one of the first two conditions is met. I don't really want and I also can't specify the value that E[I] takes, because it depends on other variables like i and sigma etc. I really only want to point out, that there are two cases in which E[I] becomes negative, otherwise positiv. If I have managed to do that with the above, then I am happy enough