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 -> infinity
