What would be the most potent free CAS for mathematical statistics?

Question

I am looking for a free CAS (Computer Algebra System) that is most able to do mathematical statistics. I thought of SAGE, but it doesn't seem to be very powerful.

It can't derive t-distribution : http://ask.sagemath.org/question/1485/student-t-pdf

And it seems to have trouble calculating even the mean and the variance of Laplace distribution!

Here's sage input/output.

INPUT:

def f1(x,mu,sigma):
  return 1/sqrt(2*pi*sigma^2)*exp(-1/2*((x-mu)/sigma)^2)
def f2(x,mu,sigma):
  return 1/sqrt(2*sigma^2)*exp(-sqrt(2)*abs((x-mu)/sigma))

var("mu sigma")

integral(x*f2(x,mu,sigma), x, -oo,oo)

OUTPUT:

1/2*sqrt(2)*integrate(x*e^(-sqrt(2)*abs(-mu + x)/sigma), x, -Infinity,
+Infinity)/sigma

INPUT:

integral(x*f1(x,mu,sigma), x, -oo,oo)

OUTPUT:

mu

INPUT:

integral((x-mu)^2*f2(x,mu,sigma), x, -oo,oo)

OUTPUT:

1/2*sqrt(2)*integrate((mu - x)^2*e^(-sqrt(2)*abs(-mu + x)/sigma), x,
-Infinity, +Infinity)/sigma

INPUT:

integral((x-mu)^2*f1(x,mu,sigma), x, -oo,oo)

OUTPUT:

sigma^2

Does anyone know free CAS which can calculate t-distribution and the mean and the variance of Laplace distribution with parameters unkown?