The$Normal$Distribution - University of Colorado Boulder
5
The Normal Distribution
(Ch 4.3)
The Normal Distribution
The normal distribution is probably the most important distribution in all of probability and statistics. Many populations have distributions that can be fit very closely by an appropriate normal (or Gaussian, bell) curve. Examples: height, weight, and other physical characteristics, scores on various tests, etc.
2
The Normal Distribution
Definition
A continuous r.v. X is said to have a normal distribution with parameters ? and > 0 (or ? and 2), if the pdf of X is
( ; )= p1
( x
)2 2 ?/
2
where
f x ?,
2e
1
1
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