Math 20. Discrete Probability

Summer 2010

Homework

The latest homework will always appear on top.

Friday August 20, 2010

Do: none
Practice: From Section 11.3: 1, 2, 3(a,c. NOT b), 5(a,b. NOT c).
Read: The Class notes. Section 11.3 discusses the same topics, but in the generality of Ergodic Chains. It may be confusing to compare notes to the text, so I reccomend the notes almost primarily for this topic.

Wednesday August 18, 2010

Do: none
Practice: From Section 11.2: 9,13,15. Also, go back and do the problems from Monday August 16,2010, but do NOT ignore NR
Read: Section 11.2 through to the end.

Monday August 16, 2010

Do: none
Practice: From Section 11.2: 5,6,7. On all problems can skip NR for today.
Read: Section 11.2 through "Time to Absorption." Stop at "Absorption Probabilities."

Friday August 13, 2010

Do: From Section 11.1: 11. From Section 11.2:1 (Hand in Wednesday August 18th)
Practice: From Section 11.2: 1,3. (practice on Matlab... hardly any coding required).
Read: Section 11.2 through "Probability of Absorbtion." Stop at "The Fundamental Matrix."

Wednesday August 11, 2010

Do: From Section 11.1: 4,12,18. (Hand in Wednesday August 18th)
Practice: From Section 11.1: 9,13 (practice on Matlab... hardly any coding required).
Read: Section 11.1 through to the end. Read especially the examples.

Monday August 9, 2010

Do: From Section 11.1: 7, 8. (Hand in Wednesday August 18th)
Practice: From Section 11.1: 17. ANY MATRIX MULTIPLICATION PROBLEMS YOU CAN FIND. Try this tutorial/practice sheet (Scroll down to "How to Multiply Matrices" for the express tutorial.
Read: Section 11.1 through EXAMPLE 11.2. Stop at the paragraph before Theorem 11.2 which starts with "We now consider the long-term behavior of a Markov Chain..."

Friday August 6, 2010

Do: From Section 9.2: 15 (just find X_n such that the variance of their sum does not tend to infinity; you need notshow that their sum's distribution is asymptotic to the standard normal density). (Hand in Wednesday August 18th)
Practice: From Section 9.2: 13.
Read: Section 9.2 through to the end.

Wednesday August 4, 2010

Do: From Section 9.2: 1(a),2,6,9. From Section 8.1:12 (using Theorem 9.4--the general Central Limit Theorem)(Hand in Wednesday August 18th)
Practice: From Section 9.2: 5,7.
Read: Section 9.2 through page 345. Stop at The Normal Distribution and Genetics.

Monday August 2, 2010

Do: From Section 9.2: 1(b). (Hand in Wednesday August 11th)
Practice: From Section 9.2: 3.
Read: Section 9.2 through page 342. Stop at Theorem 9.4 (Central Limit Theorem) of page 343.

Friday July 30, 2010

Do: From Section 9.1: 6, 8, 14 . (Hand in Wednesday August 11th)
Practice: From Section 9.1: 7, 9, 11.
Read: Section 9.1 through to the end. Historical Remarks encouraged.

Wednesday July 28, 2010

Do: From Section 9.1: 1. (Hand in Wednesday August 11th)
Practice: Familiarize yourself with the programs from class today. From Section 9.1: 4 (just the Chebyshev estimation)
Read: Section 9.1 through Theorem 9.1. Stop after Reading the statement of the Central Limit Theorem.

Monday July 26, 2010

Do: From section 8.1: 15. From section 9.1: 2 (Hand in Wednesday August 4th)
Practice:From section 8.1: 12 (hard), 14.
Read: Section 5.2 page 212 (just read the first three paragraphs of "Normal Density"). Section 9.1 through "Standardized Sums" (this is only about 1 page).

Friday July 23, 2010

Do: From section 8.1: 4, 8 (you may reference the appropriate example/demonstration in class) (Hand in Wednesday August 4th)
Practice:From section 8.1: 9, 11, 13.
Read: Section 8.1 through to the end. Historical Remarks ARE assigned (they are usually just suggested).

Wednesday July 21, 2010

Do: From section 8.1: 1, 2 (only need to write an "intuitive program" and need not run it), 6, 7 (Hand in Wednesday August 4th)
Practice:From section 8.1: (for computer folk interested in a cool experiment) 2 & 3, (for non programmers) 5.
Read: Section 8.1 through page 306. Stop at Law of Large Numbers.

Monday July 19, 2010

Do: From section 5.1: 6, 10, 16, 18, 28. (Hand in Wednesday July 28th)
Practice:From section 5.1: 17, 19, 25
Read: Section 5.1 through to the end.

Friday July 16, 2010

Do: From section 5.1: 1,9. From section 1.2: 22. (Hand in Wednesday July 28th)
Practice:From section 5.1: 11
Read: Section 5.1 through page 189. Stop at example 5.4.

Wednesday July 14, 2010

Do: From section 6.1: 12. From section 6.2: 4, 8. (Hand in Wednesday July 21st--abbreviated due to exam.)
Practice:From section 6.2: 3, 13
Read: Section 6.2 through to the end.

Monday July 12, 2010

Do: From section 6.1: 14, 16, 20(a,b) (Hand in Wednesday July 21st)
Practice:From section 6.1: 9, 13, 19
Read: Section 6.1 through to the end; read especially "Records," "Craps," "Roulette," and "Martingales." Historical Remarks optional; skip "Poisson Distribution".

Friday July 9, 2010

Do: From section 4.1: 36, 48, 63(a). From section 6.1: 2, 8 (Hand in Wednesday July 21st)
Practice: From section 4.1: 33, 17, 23. From section 6.1: 1, 5.
Read: Section 6.1 through page 230; stop at "The Sum of Two Random Variables".

Wednesday July 7, 2010

Do: From section 3.2: 15. From section 4.1: 4, 8, 22 (Hand in Wednesday July 14th)
Practice: From section 4.1: 3, 5, 9, 19, 29
Read: Section 4.1 through page 144; stop at "Independent Trials Processes".

Friday July 2, 2010

Do: From section 3.1:4,12. From section 3.2: 18, 26 (Hand in Wednesday July 14th)
Practice: From section 3.2: 13,19
Read: Section 3.2 to the end. Historical Remarks recommended but optional. Read 4.1 through page 135; stop at "Bayes Probabilities."

Wednesday June 30, 2010

Do: From section 3.2: 2,6,10,24 (Hand in ~~Wednesday July 7th~~ Friday July 9th)
Practice: From section 3.2: 1,3,9,21
Read: Section 3.2 through page 103 esp. Hypothesis Testing; stop at "Inclusion-Exclusion Principle".

Tuesday June 29, 2010

Do: From section 3.1: 16 (Hand in ~~Wednesday July 7th~~ Friday July 9th)
Practice: From section 3.1: 9
Read: Section 3.1 to the end. Historical Remarks recommended but optional.

Monday June 28, 2010

Do: From section 1.2: 31. From section 3.1: 3, 5, 10(Hand in ~~Wednesday July 7th~~ Friday July 9th)
Practice: From section 3.1: 1, 2, 6, 13, 14(a)
Read: Section 1.2 to the end. Historical Remarks optional. Section 3.1 through page 81; stop at "Generating Random Permutations."

Friday June 25, 2010

Do: From section 1.2: 1, 6, 10 (Hand in ~~Wednesday July 7th~~ Friday July 9th)
Practice: From section 1.2: 2, 4, 5, 7, 8, 18, 29 (requires infinite sample space. will return to this later)
Read: Section 1.1, and Section 1.2 through page 24; stop at "Tree Diagrams."