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Math Help - Define f for all x... (Convergence, integration... (Rectangular distribution?)

  1. #1
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    Post Define f for all x... (Convergence, integration... (Rectangular distribution?)

    Hey mathematicians,

    I have a question, which I hoped someone in this forum could help me solve...

    It goes as follows...

    Define f for all x by f(x) = 1/(a-b) for x ∈ (belongs to) [a,b], f(x) = 0 for x does not belong to [a,b].

    (In statistics it is called rectangular distribution)



    Integral from range -infinite to +infinite = x^2 f(x) dx




    I'm very sorry about the missing math operators...
    I'm still searching for a solution to copy images in here...
    It would make it a lot easier!

    In hope of a help... Many thanks...
    Simon DK
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sh01by View Post
    Hey mathematicians,

    I have a question, which I hoped someone in this forum could help me solve...

    It goes as follows...

    Define f for all x by f(x) = 1/(a-b) for x ∈ (belongs to) [a,b], f(x) = 0 for x does not belong to [a,b].

    (In statistics it is called rectangular distribution)



    Integral from range -infinite to +infinite = x^2 f(x) dx




    I'm very sorry about the missing math operators...
    I'm still searching for a solution to copy images in here...
    It would make it a lot easier!

    In hope of a help... Many thanks...
    Simon DK
    Define:

    <br />
f(x)=\left\{ {1/(b-a),\ \ \ x \in [a,b] \atop 0,\ \ \ \mbox{otherwise}} \right.<br />

    Then:

    <br />
\int_{-\infty}^{\infty} x^2\ f(x)\ dx=\int_{a}^{b} x^2/(b-a)\ dx<br />

    RonL
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  3. #3
    Junior Member
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    Nov 2006
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    Copenhagen
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    Smile Thanks, I solved two similar questions using your solution...

    Hey Cpt. Black,

    Thanks, it was a big help...

    You pasted what seems to be LaTeX, but - when I preview a post it seems it doesn't show up as 'real' math... Only LaTeX language? Why is that?

    Simon DK
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by sh01by View Post
    Hey Cpt. Black,

    Thanks, it was a big help...

    You pasted what seems to be LaTeX, but - when I preview a post it seems it doesn't show up as 'real' math... Only LaTeX language? Why is that?

    Simon DK
    This site has a LaTeX add-in, which renders LaTeX code between [tex][/tex] tags as graphics which are embedded in the displayed text.

    See this.

    (Note there are some bugs, so that you can lose your stuff if you post
    or preveiw and there is an error in the LaTeX - work around is to copy
    everything to the copy/paste buffer before preview or pose (select all
    abd [cntrl]c)

    RonL
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