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Solving Distribution Functions

  1. Apr 13, 2010 #1
    1. The problem statement, all variables and given/known data

    Given the distribution function:

    f(x) = A*sin^2(pi*x/L) for 0 < x < L
    = 0 for x elsewhere

    Find the values for:
    A, mean x (x), most probable x (xmp) and root mean square x (xrms)

    2. Relevant equations



    3. The attempt at a solution

    The professor has not shown us how to do a problem like this. So I am lost.

    My guess at solving A would be to take the integral of f(x) and set it equal to 1. But I do not know what limits I should use on the integral (0 to inf or 0 to L?).

    I think the most probable x would be + or - 1 standard deviation from the mean value? I don't know how to solve for that either.

    Thanks in advance for the help!
     
  2. jcsd
  3. Apr 13, 2010 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    When in doubt, go back to the definitions.

    For starters, for a normalized distribution, [itex]f(x)[/itex] , you have

    [tex]\int_{-\infty}^{\infty}f(x)dx=1[/tex]

    In this case, [itex]f(x)[/itex] is zero for most of the interval, and so the only non-zero contribution to this integral comes on the interval [itex]0[/itex] to [itex]L[/itex]...What does that give you for [itex]A[/itex]?

    What are the definitions of "most probable value" and "root mean square x"?...Apply those definitions.
     
  4. Apr 13, 2010 #3
    Does that mean I should integrate from 0 to L and normalize to 1 to solve for A?

    I don't know what the 'definitions' are. Like I said, my professor did not teach this. That is why I am asking for help here. Could you provide a little more insight? Should I integrate x*f(x) to get the most probable value of x?
     
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