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Unformatted text preview: on of Normal distribution (Normal pdf )
is deﬁned by
(x−µ)2
1
f (x) = √ e− 2 2 ,
2⇡ where is the population standard deviation; ⇡ = 3.1415926; e = 2.71828 is the base of the
natural log; µ is the population mean.
Remark. Notice that two parameters, µ and uniquely deﬁnes the distribution. Assuming the underlying distribution is Normal with mean µ and standard deviation ,
then given any value x, the pdf gives the density of distribution at the outcome x.
By calculating the area below the pdf, we can ﬁnd the probability of di↵erent events.
To see a more visual demonstration, go to http://demonstrations.wolfram.com/search.
html?query=Normal%20distribution.
29 EC 271
3.2.2 Applied Statistical Methods: Lecture Notes (Leshui He) 2014 Putting the PDF to Work: Standard Normal Distribution Deﬁnition. The standard normal distribution is the the normal distribution with mean
µ = 0 and standard deviation = 1.
Mathematicians have cal...
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 Fall '13
 Alexandru
 Probability

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