For my statistical mechanics class I need to find the cumulants of a special distribution of which all moments are constant and equal to a. I followed two different approaches and obtained imcompatible results, something is wrong but I couldn't figure it out.
Here's what I did:
Since all...
Yeah, as I said I got the idea of integrating odd functions between -a and a, thank you very much. I solved my problem.
I tried to tell that I already did that substitution in my posting number 4. But I couldn't evaluate that integral either. I mistakenly argued that since u=x^2, I can say...
I got it arildno, thanks very much.
Could you also tell me how to search for the integrals before posting them here? I tried to use the latex code of the integral but it didn't help.
I see, I am expected to show my own work when posting a question here. Actually that integral is just a small part of an answer to calculate the first four moments of a gaussian distribution with direct integration of the pdf.
I tried to re-write the integral as...
Hi,
I'm trying to show the following equation is correct:
\int_{-\infty}^{\infty}x^{3}e^{-x^2}dx = 0
I obtained the result as 0 using Mathematica but couldn't figure out a way to evaluate the integral.
I am just an unfortunate computer scientist who happens to follow a graduate...