STAT 3743 Daily Outline
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Mean and variance of X-bar
MGF of linear combination of independent sample
MGF of X-bar
Example: SRS(11) from gamma, find dist'n of X-bar
Proposition: SRS(n) from norm, then X-bar 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
- X-bar and S2 are independent
-
S2 is scaled
chisqwithdf= n - 1
Linear combinations of independent normals is normal, too
Central Limit Theorem
statement of the theorem
Remarks:
- if X's are normal, then X-bar is normal
- if X's are close to normal, then X-bar is close to normal, too
- Discrete/continuous doesn't matter
- how large is large?
Date: 2010-11-05 14:44:11 EDT
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