Mode of a probability distribution

[indie452]

Homework Statement

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

Homework Equations

p(L)dL = A \frac{L}{i}^aexp(-\frac{L}{i}) \frac{dL}{i}

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

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
\int L p(L)dL

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 doesn't have a peak like on gaussian like plots

 

[Spinnor]

If this question is more astronomy or math then physics you might try in the astronomy or math section of Physics Forums. A Google search of the exact phrase "luminosity probability distribution" yields 5 hits.


http://www.google.com/webhp?hl=en#h...w.,cf.osb&fp=dc20b2672385f007&biw=720&bih=426

Good luck.