Weekly class schedule (tentative):
「課程主題」 「課程內容與指定閱讀」 「教學活動與作業」
1. The weak law of large numbers, the strong law of large numbers section 1 in-class exercise
2. Probability measures, Lebesgue measure on the unit interval section 2 homework 1
3. measurable sets, nonmeasurable sets section 4 in-class exercise
4. Denumerable probabilities, limit sets, Borel-Cantelli lemmas section 4 homework 2
5. Simple random variables section 5 in-class exercise
6. The law of large numbers revisit section 6 homework 3
7. Markov Chains, Chernoff's theorem section 8 in-class exericse
8. The law of the iterated logarithm, measurable functions seciont 9 homework 4
9. midterm
10. Distribution functions, weak convergence section 12 in-class exercise
11. Integral, Integration to the limit, uniform integrability section 13 homework 5
12. Integral with respect to Lebesgue measure section 15 in class exercise
13. Product measure and Fubini theorem section 16 homework 6
14. Convergence of distributions section 17 in-class exercise
15. Conditional expectation and martingales section 30 homework 7
16. final exam
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