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Determining the normalization constant C

  1. Feb 12, 2013 #1
    1. The problem statement, all variables and given/known data
    Consider the distribution function F(x) = Cexp(-ax)

    Find the normalization constant C


    2. Relevant equations

    3. The attempt at a solution

    This is more clarification since this is not actually a homework problem but was in my profs notes. He started with the distribution function above and said we were to determine C.

    He then gave us the average equation below:
    <z> = ∫ z f(z) dz / ∫ f(z) dz

    Which in this case would be xexp(-ax) / exp(-ax)

    I am a little confused as to how you are able to determine the constant C if you determine the average of the system/distribution.
     
  2. jcsd
  3. Feb 12, 2013 #2

    vela

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    If a distribution is normalized, that means
    $$\int f(z)\,dz = 1,$$ where the integral is taken over the entire range of z. In this case, the formula for the average simplifies to
    $$\langle z \rangle = \int z f(z)\,dz.$$ The formula your professor gave works for the case where f(z) isn't normalized.

    To normalize the F(x) you've been given, you want to find the value of C such that the first integral holds.
     
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