ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 21 Jan 2012 02:07:56 -0600Symbolic expectations and double integralshttps://ask.sagemath.org/question/8648/symbolic-expectations-and-double-integrals/I'd like to compute the following expectation ($U$ and $V$ are independent and normally distributed or Gaussian)
$a_{k,p}=E(|U|^p|U+\sqrt{k-1}V|^p)$
Is there a way to directly compute those expectations in Sage ?
If I write it down, I obtain a double integral which I already tried to compute with maxima like this (ok here, you can only see the starting point with the inner integral with respect to $v$ first)
load(distrib);
n(x):=pdf_normal(x, 0, 1);
inner_integral: integrate(abs(u+sqrt(k-1)*v)^p*n(v), v, minf, inf);
but to no avail.
NB: The absolute central moment $a_{1,p/2}$ can be easily obtained with maxima with
ratsimp(integrate(abs(x)^p*n(x), x, minf, inf));
but no 'simple' expression as for the aforementioned double integral.
Any hint?Green diodSat, 21 Jan 2012 02:07:56 -0600https://ask.sagemath.org/question/8648/