Recent content by areslagae

Hi all, I have a quick additional question. A colleague pointed out to me that the cited paper only proves the theorem from my first post in the case that Y is defined over [0,a]. However, the random variables (X + Y) mod a and (X + (Y mod a)) mod a have the same distribution...

Thanks for both your replies! At first, me (and my collegues) found this result somewhat counter-intuitive. It seems that you do not, but you most likely you have a deeper intuition. Meanwhile, I also found the following paper which is interesting in this context: The Distribution Functions...

If X is uniformly distributed over [0,a), and Y is independent, then X + Y (mod a) is uniformly distributed over [0,a), independent of the distribution of Y. Can anyone point me to a statistics text that shows this? Thanks,

I actually mean division. So, if E[X] = 0, does E[Y/X] = 0 follow, for Y independent of X? Additionally, I have that X is symmetric. Intuitively, it seems that this does hold. E[Y/X] = E[Y] E[1/X] (X and Y are independent) So, it remains to be shown that, if E[X]=0, and X is symmetric, then...

E[x] = 0 => e[y/x] = 0 ? (division, not cond prob) I have E[X] = 0. Does this imply that E[Y/X] = 0, for Y independent of X?

Hello all, I am trying to solve an integral with Mathematica, but I do not succeed. I am wondering whether the integral cannot be solved, or whether Mathematica cannot solve the integral, or whether I am doing something wrong. Details: * Mathematica does not seem to be able to solve the...

The integral assume(a > 0); int(exp(a*cos(phi))*sin(phi)^2, phi = 0 .. Pi); equals to (Pi/a)*BesselI(1,a) I have solved the integral using Mathematica, which seems to solve all these integrals out of the box.

Thanks! Apparently, Mathematica is the only program that can solve several of the integrals I am dealing without of the box. Unfortunately, I do not have access to Mathematica. Would you please be so kind to try if Mathematica can solve int(exp(a*cos(phi))*(sin(phi))^2, phi = 0 .. Pi) with a...

Thanks. Is "4-D spherical coordinates" established terminology? Is this the "standard" transformation? I guess there are other ones?

I am looking for a 4D angular coordinate system (radius and three angles) and its corresponding "hypervolume element". 2D: polar coordinates - dA = r dr dtheta 3D: spherical coordinates - dV = r^2 sin(phi) dphi dtheta dr 4D: ?

I am trying to solve int(int(exp(a*cos(theta)*sin(phi))*sin(phi), phi = 0 .. Pi), theta = 0 .. 2*Pi) (1) with a a constant. Using the second last definite integral on http://en.wikipedia.org/wiki/List_of_integrals_of_exponential_functions the integral (1) reduces to...