1
AMS412
Professor Wei Zhu
Sampling from the Normal Population
*
Example
: We wish to estimate the distribution of heights of adult US male. It is
believed that the height of adult US male follows a normal distribution
Def.
Simple random sample: A sample in which every subject in the population
has the same chance to be selected.
X
:
The Random Variable denote the height of a adult male we will choose
randomly from the population
So
: the distribution of a randomly selected subject is the population
distribution.
Theorem 1
Sampling from the normal population
Let
, where i.i.d stands for independent and identically
distributed
1.
2.
A function of the sample variance as shown below follows the Chi square
distribution with (n1) degrees of freedom:
*Reminder: The Sample variance
is defined as:
*Def 1: The Chisquare distribution is a special gamma distribution (***
Please find out which one it is.)
*Def 2: Let
, then
3.
are
independent
.
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 Spring '14
 Normal Distribution, Variance, Chi Square Distribution

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