Gaussain distribution

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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