ST2004 - Applied Probability I 

2017/2018


Change of schedule for week 3: the class of Wednesday 11/10/17 has been postponed to Thursday 12/10/17, 4pm-5pm, Room LB107.


Module Code: ST2004

Module Title: Applied Probability I (module descriptor)

Credit Value: 5

Cohorts: MSISS, CSL(JS)

Week range: 05-10, 12-16 

Semester: S1 (Michaelmas) 

Total hours: 33


Timetable:

- Monday, h. 9am-10am, ICTLAB1

- Tuesday, h. 5pm-6pm, room LB08

- Wednesday, h. 3 pm-4pm, room LB04


Calendar of lab sessions:

Lab sessions are scheduled on Monday morning. As for the first six weeks, labs are scheduled for:

- Monday 2/10/17

- Monday 9/10/17

- Monday 16/10/17 (cancelled)

- Monday 23/10/17


Textbook: Tijms, "Understanding Probability" (pages indicated below refer to 3rd edition).

Additional material will be provided when needed.


Material:

26/09/17: slides (pdf)

27/09/17: slides (pdf)

02/10/17: lab (pdf,xlsx)

03/10/17: slides (pdf)

09/10/17: lab (pdf,xlsx)

04/10/17, 10/10/17, 12/10/17: doc-cam notes (encrypted pdf)

17/10/17: slides (pdf), spreadsheet (xlsx)

23/10/17: lab (pdf,xlsx)



Syllabus (lecture by lecture):

26/09/17: Monte Carlo approach, Empirical Law of Large Numbers, Birthday problem (via both simulation and combinatorics).

Textbook: Section 2 (pp. 18-25), Section 3 (pp. 75-80, 3.1.4 excluded).

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27/09/17: True and pseudo random number generation, Multiplicative congruential method, Random generation from an interval, Random generation from integers, Generation of random permutations.

Textbook: Section 2.8 (pp. 52-59), Section 2.9.4 (pp. 62-63).

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02/10/17: Lab 1 - generating random passwords.

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03/10/17: More on generation of random permutations, 1970 draft lottery problem.

Textbook: Section 2.8.1 (pp. 55-56), Section 3.7 (pp. 98-102).

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04/10/17: Frequentist probability, Axiomatic foundations of probability.

Textbook: Chapter 7, Section 7.1 (pp. 229-232).

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09/10/17: Lab 2 - does skill win the league?

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10/10/17: Definition of probability functions on a finite or countably infinite sample space, Equally likely events, Examples.

Textbook: Section 7.1.1 (pp. 232-235). 

Assignment: Problems 7.1-7.5 and 7.14 (if you want them to be checked -not marked- hand your solutions in on Wednesday 18/10/17).

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12/10/17: Probability on an uncountable sample space (dartboard example)Derivation of basic rules of probability from axioms, Independent events.

Textbook: Example 7.3 (pag. 234), Section 7.2 (pp. 239-241, 7.2.1 excluded), Section 7.3 (pp. 243-244). 

Assignment: Probl. 7.27 and 7.28 (if you want them to be checked -not marked- hand your solutions in on Wednesday 18/10/17).

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17/10/17: Monty Hall problem via simulation, Conditional probability, Chain rule, Bayes rule.

Textbook: Chapter 6 (pp. 212-217, 6.1.3 excluded, pp. 220-222), Chapter 8 (pp. 256-258, pp. 260-261). 

Assignment: Problems 8.1-8.3 (if you want them to be checked -not marked- hand your solutions in on Tuesday 31/10/17).

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