
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
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  
Member Joined: Aug 2009 From: Copenhagen, Denmark Posts: 45 Thanks: 0  Re: Probabilities in the normal distribution Quote:
 

Tags 
distribution, normal, probabilities 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Multivariate normal distribution and marginal distribution  nakys  Advanced Statistics  0  October 3rd, 2013 09:27 AM 
normal distribution??  pomazebog  Algebra  8  April 15th, 2012 08:56 PM 
Normal distribution  hoyy1kolko  Algebra  1  August 8th, 2011 02:49 AM 
Normal distribution...  hoyy1kolko  Algebra  8  July 7th, 2011 12:37 AM 
Normal Distribution  symmetry  Advanced Statistics  1  June 28th, 2007 02:44 PM 