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May 14th, 2012, 11:45 AM   #1
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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?
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May 14th, 2012, 01:36 PM   #2
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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.
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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
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