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Unformatted text preview: distribution,”
which is read aloud as “the normal µ, σ 2 distribution.” Later in this section it is shown that the
pdf integrates to one, the mean is µ, and the variance is σ 2 . The pdf is pictured in Figure 3.10. The
" 1
2! " 68.3% " 13.6% 2.3% µ
Figure 3.10: The Gaussian (or normal) pdf
parameter µ is sometimes called the location parameter, because the pdf is symmetric around the
value µ. The eﬀect of replacing µ by µ + 3, for example, would be to slide the pdf to the right by
three units. The parameter σ is sometimes called the scale parameter. As indicated in the ﬁgure,
the width of the graph of the pdf is proportional to σ. For example, about 68.3% of the probability
mass is in the interval [µ − σ, µ + σ ] and roughly 95% (more precisely, 95.44%) of the distribution
is in the interval [µ − 2σ, µ + 2σ ]. The peak height of the pdf is √ 1 2 . The height is inversely
2πσ
proportional to σ as expected, so for small σ the graph is tall and narrow, and for large σ it is short
and spread out, but for all σ the area under the pdf is one.
The standard normal distribution is the normal dis...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.
 Spring '08
 Zahrn
 The Land

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