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 November 27th, 2007, 11:29 PM #1 Newbie   Joined: Oct 2007 Posts: 15 Thanks: 0 help pls !!! asap prove that one over square root of two pi times the integral of e raise to negative one half x squared, dx from positive infinity to negative infinity is equal to one.
 November 28th, 2007, 07:00 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms The integrand is the normal distribution's pdf. The fact that the integral is 1 means that there's a 100% chance of a normally distributed value falling from -infty to +infty. you can probably Google for a proof.
November 28th, 2007, 02:54 PM   #3
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Re: help pls !!! asap

Quote:
 Originally Posted by haruka-san prove that one over square root of two pi times the integral of e raise to negative one half x squared, dx from positive infinity to negative infinity is equal to one.
The simplest proof involves squaring the integral, so that it is a double integral in x and y, then convert to polar coordinates. This integral can be evaluated anaytically.

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