MA/STAT416: Probability
Lecture Notes
Spring 2011
1
Chapter 9: The Normal Distribution
April 21, 2011
9
The Bell Shape Distribution
9.1
History
The normal distribution is the most common, popular model for continuous random
variables. Data collected on many types of random variables in daily life approximately
follow normal distribution. This empirical phenomenon can be partially explained by
means of mathematical theorems. But some of it is still a mystery. Another reason for
historical importance of the normal distribution is that many methods that statisticians
use are based on the assumption that the random variable in consideration has a normal
distribution. Normal distributions are characterized by two parameters, the mean
μ
, and
variance
σ
2
.
If we know these two quantities, then any probability can be calculated
for normal distributions. If
X
is a random variable, we say
X
∼
N
(
μ, σ
).
If
μ
= 0
and
σ
= 1, then the distribution is called standard normal. A random variable having
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 Spring '08
 Staff
 Normal Distribution, Probability, Standard Deviation, Variance, Probability theory, probability density function

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