Math3200 Intermediate
Probability and Statistics
Prof. Nan Lin
Department of Mathematics
Washington University

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Populations, Samples, Parameters, and Statistics

Outline
•
Sampling distribution of the sample mean
–
Central limit theorem
–
Normal approximation of binomial
–
Continuity correction
•
Sampling distribution of the sample mean
–
Chi-square distribution

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What we learned before
•
?
=
1
𝑛
?
𝑖
𝑛
𝑖=1
•
If
?
?
𝑖
= ?
𝑖
,
?
?
=
1
𝑛
?
𝑖
𝑛
𝑖=1
•
If
??𝑟
?
𝑖
= 𝜎
𝑖
2
and
?
𝑖
are mutually independent,
??𝑟
?
=
1
?
2
𝜎
𝑖
2
𝑛
𝑖=1
•
If
?
𝑖
are mutually independent with mean
?
?
𝑖
= ?
and
??𝑟
?
𝑖
= 𝜎
2
,
?
?
= ?, ??𝑟
?
=
𝜎
2
?
•
If
?
𝑖
are i.i.d.
𝑁(?, 𝜎
2
)
?
=
1
?
?
𝑖
𝑛
𝑖=1
~𝑁(?,
𝜎
2
?
)