ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 10 Oct 2021 16:50:45 +0200Gaussain distributionhttps://ask.sagemath.org/question/59317/gaussain-distribution/ One of the fundamental statistical distribution functions is the Gaussian density function
f(x)=(1/√(2π)) e^(x^2/2)
(a) Use a computer program (i.e. Mathematica) to evaluate the definite integral
integral f(x)dx, from -n to n
for n = 1, 2, 3. Can you exploit a symmetry property of the function f to simplify such evaluations?
(b) Give a convincing argument that
Integral f(x)dx = 1, from negative infinity to infinity
Hint:Show that 0< f(x)<e^(x^2/2) forx>1 and for b>1
Lim (Integral e^(-x^2/2)dx = 0, from b to infinity) as b -> infinityJCMSun, 10 Oct 2021 16:50:45 +0200https://ask.sagemath.org/question/59317/