Gaussain distribution

asked 2021-10-10 16:50:45 +0200

JCM gravatar image

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

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This looks like homework.

If you want some help, you should ask more precise questions related to your research in solving those exercises, especially where you are locked.

tmonteil gravatar imagetmonteil ( 2021-10-10 23:10:54 +0200 )edit