(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Homework Help: Mode of a probability distribution

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