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Math Help - case by case analysis

  1. #1
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    case by case analysis

    Hi,

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


    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"

    Thanks
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  2. #2
    Super Member
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    Re: case by case analysis

    The use of "for" and "and" is correct but  <0, <0, \geq 0 should be the number(s) that E[I] takes under the conditions described.
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  3. #3
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    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
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