ELEC 303 – Random Signals Lecture 14 – Sample statistics, Limit Theorems Dr. Farinaz Koushanfar ECE Dept., Rice University Oct 21, 2010.

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Presentation transcript:

ELEC 303 – Random Signals Lecture 14 – Sample statistics, Limit Theorems Dr. Farinaz Koushanfar ECE Dept., Rice University Oct 21, 2010

Outline Sample statistics – Mean, variance, median, quantile Laws of large numbers Central limit theorem

Statistics

Sample mean and median

Sample median (cont’d)

Percentile

Why is percentile useful?

Variability measuring

Sample variance and standard deviation

Usages

Limit theorems

Law of large numbers

WLLN

Recall

WLLN

Sum of independent RV’s

Central Limit Theorem

Normal approximation to Binomial

Example: Polling

Example: Polling (Cont’d)

Limit Theorem

Strong Law of Large Numbers

Review of Law of Large Numbers

What does LLN Imply?