# Homework Help: Mode of a probability distribution

1. Oct 23, 2011

### indie452

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 $\frac{L}{i}^a$exp(-$\frac{L}{i}$) $\frac{dL}{i}$

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
$\int L p(L)dL$

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 doesnt have a peak like on gaussian like plots

2. Oct 23, 2011