STAT 3743 Daily Outline
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Mean and variance of Xbar
MGF of linear combination of independent sample
MGF of Xbar
Example: SRS(11) from gamma
, find dist'n of Xbar
Proposition: SRS(n) from norm
, then Xbar is normal, too
Sum of independent chisq
is chisq
, and df
's add
Sum of squared standard normals is chisq
with df
= n
Theorem: SRS(n) from norm
, then
 Xbar and S^{2} are independent

S^{2} is scaled
chisq
withdf
= n  1
Linear combinations of independent normals is normal, too
Central Limit Theorem
statement of the theorem
Remarks:
 if X's are normal, then Xbar is normal
 if X's are close to normal, then Xbar is close to normal, too
 Discrete/continuous doesn't matter
 how large is large?
Date: 20101105 14:44:11 EDT
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