Week_10_Slides

# Week_10_Slides - Week 10 Central Limit Theorem Point...

This preview shows pages 1–7. Sign up to view the full content.

Week 10 Central Limit Theorem Point Estimation

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Lindeberg-Levy Central Limit Theorem (CLT) Suppose that 1 2 , ,... X X are iid rv’s with finite mean , finite variance 2 and a mgf. Let 1 1 n n i i X X n and / n n X U n . Then N(0,1) d n U   .
Steps to Prove the CLT

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The Uniqueness Theorem Suppose that 1 2 , , ,... X X X are rv’s with cdf’s 1 2 ( ), ( ), ( ),. .. F x F x F x , respectively, an d mgf’s 1 2 ( ), ( ), ( ),. .. m t m t m t , respectively, such that ( ) ( ) n m t m t as n   t    . Then ( ) ( ) n F x F x x    .
Variance Estimated CLT N(0,1) / d n n n X W S n   as n  

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Suppose that 1 2 , ,... X X are iid rv’s with finite mean , finite variance 2 and a mgf. Let 1 1 n n i i X X n (sample mean) and 2 2 1 1 ( ) 1 n n i i S X X n (sample variance). n  
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 24

Week_10_Slides - Week 10 Central Limit Theorem Point...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online