July 2012
Intermediate to advanced
400 pages
9h 33m
English
Content preview from Statistical Inference: A Short CourseBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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6.2 The Normal Distribution
A continuous random variable 
has a normal distribution if its probability density function is bell-shaped, symmetrical about its mean 
, and asymptotic to the 
or horizontal axis (Fig. 6.3) In what follows, we shall refer to the normal probability density function as simply the “normal curve.” Asymptotic to the horizontal axis means that the normal curve extends from 
with its tails gradually approaching, but never touching, the horizontal axis. The normal probability distribution is completely determined once its mean 
and standard deviation 
are given. In this regard, if 
follows a normal distribution with a known mean and standard deviation, then we will write:
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