# Thread: Define f for all x... (Convergence, integration... (Rectangular distribution?)

1. ## 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

2. Originally Posted by sh01by
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:

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

Then:

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

RonL

3. ## 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

4. Originally Posted by sh01by
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  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