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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 on theme: "ELEC 303 – Random Signals Lecture 14 – Sample statistics, Limit Theorems Dr. Farinaz Koushanfar ECE Dept., Rice University Oct 21, 2010."— Presentation transcript:

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

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

3 Statistics

4 Sample mean and median

5 Sample median (cont’d)

6 Percentile

7 Why is percentile useful?

8 Variability measuring

9 Sample variance and standard deviation

10 Usages

11 Limit theorems

12 Law of large numbers

13 WLLN

14 Recall

15 WLLN

16 Sum of independent RV’s

17 Central Limit Theorem

18 Normal approximation to Binomial

19

20 Example: Polling

21 Example: Polling (Cont’d)

22

23

24

25 Limit Theorem

26 Strong Law of Large Numbers

27 Review of Law of Large Numbers

28 What does LLN Imply?

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