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Mode of a probability distribution

  1. Oct 23, 2011 #1
    1. The problem statement, all variables and given/known data

    I have a luminosity prob distribution that i want to plot and find the expectation value and mode for.

    2. Relevant equations

    p(L)dL = A [itex]\frac{L}{i}^a[/itex]exp(-[itex]\frac{L}{i}[/itex]) [itex]\frac{dL}{i}[/itex]

    A=const
    a= -0.7
    i= 1.4e10 solar luminosity units
    lower limit = 1e9 solar luminosity units

    3. The attempt at a solution

    I know that i can pick an arbitrarily large upper limit because as L increases much more than i, the exp term grows faster and the function goes to zero.

    the expected value is just
    [itex]\int L p(L)dL[/itex]

    but the mode is harder as usually we can differentiate the prob distribution and set it to zero to find turning point but this function plotted doesnt have a peak like on gaussian like plots
     
  2. jcsd
  3. Oct 23, 2011 #2
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