# case by case analysis

• May 14th 2013, 10:53 PM
neptunhiker
case by case analysis
Hi,

I am not sure about the notation of a case by case problem. This is my solution:

$\displaystyle E[I]=\begin{cases} <0 & \text{for}\quad l>0 \quad \text{and} \quad \mu<i\left(1-\frac{1}{l}\right)+\frac{l\sigma^2}{2}\\ <0 & \text{for}\quad l<0 \quad \text{and} \quad \mu>i\left(1-\frac{1}{l}\right)+\frac{l\sigma^2}{2}\\\geq0 & otherwise\end{cases}$

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"(Wink)

Thanks
• May 15th 2013, 03:33 AM
Shakarri
Re: case by case analysis
The use of "for" and "and" is correct but $\displaystyle <0, <0, \geq 0$ should be the number(s) that E[I] takes under the conditions described.
• May 15th 2013, 06:11 AM
neptunhiker
Re: case by case analysis
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;)