May 14th, 2012, 11:45 AM #1 Member   Joined: Aug 2009 From: Copenhagen, Denmark Posts: 45 Thanks: 0 Probabilities in the normal distribution Hello all I am writing an assignment where I, among other things, have to write about simple properties of the normal distributions. I have to describe why the form of the normal distribution changes as the variance changes, e.g. why the normal distribution flattens out. My argument is as follows: Consider a normal distribution with mean and variance . Now we look at the probability of getting a value in the interval , where . When we use the probability density function, we get that: Now, let . We get that and By using some rule of limits (?) we conclude that the limit of the normal distribution on an interval approaches 0 as . Does this statement hold? Don't pay much attention to the formulations - but does the mathematical part make sense? May 14th, 2012, 01:36 PM #2 Global Moderator   Joined: May 2007 Posts: 6,854 Thanks: 744 Re: Probabilities in the normal distribution Effectively you are showing that the normal distribution flattens out as ? gets larger. There are some errors (typos?) in your analysis. You have P(X=x) when you should have P(a < X < b) The integral limit should be b - a, not a - b. May 14th, 2012, 01:54 PM   #3
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Re: Probabilities in the normal distribution

Quote:
 Originally Posted by mathman There are some errors (typos?) in your analysis.
Thanks for the quick reply! Yes, the integral limit was a typo, while the P(X=x) was a misunderstanding.Thanks for clearing that up  Tags distribution, normal, probabilities Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post nakys Advanced Statistics 0 October 3rd, 2013 09:27 AM pomazebog Algebra 8 April 15th, 2012 08:56 PM hoyy1kolko Algebra 1 August 8th, 2011 02:49 AM hoyy1kolko Algebra 8 July 7th, 2011 12:37 AM symmetry Advanced Statistics 1 June 28th, 2007 02:44 PM

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