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February 19th, 2015, 03:30 AM   #1
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Expected value - above a certain amount - Normal Distribution

Hello guys please help me with this as I've hit the wall

I have a normal distribution with mean and standard deviation - which is fine. I can calculate the distribution and I can sample from it etc

I want to calculate the expected value of a distribution above a certain point. Does anyone know the formula for calculating this?

So if I my mean is 2000 and standard deviation of 500 what is the expected value above say 1000?

thanks
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February 19th, 2015, 04:43 AM   #2
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You mean, if X~N(2000,500) P(X>1000) or E(X|X>1000) ?
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February 19th, 2015, 04:54 AM   #3
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Thanks mehoul I think I'm after a formula to calculate E(X|X>1000)
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February 19th, 2015, 05:30 AM   #4
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So you just have to integrate the function x*f(x) where f(x) is the gaussian density (with mean = 2000 and sd = 500) from 1000 to infinity, and divide the result by P(X>1000) which is the integral of the gaussian density from 1000 to infinity.
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February 19th, 2015, 05:45 AM   #5
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Quote:
Originally Posted by mehoul View Post
So you just have to integrate the function x*f(x) where f(x) is the gaussian density (with mean = 2000 and sd = 500) from 1000 to infinity, and divide the result by P(X>1000) which is the integral of the gaussian density from 1000 to infinity.
Thanks

Any help on a simple formula to do this integration within excel/vba?
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