Friday, September 29
Permutations and combinations (Sections 1.1-1.4 just before binomial theorem).
Homework 1 (due October 5): 1, 3, 4, 7, 8, 9, 13, 15, 16, 17, 18, 20a, 21, 22.
Monday, October 2
The TA will lead this class, will discuss examples. Try as much homework problems as you can before this class.
I (R.V.) will not hold office hours this Monday, but the TA will (2:00 - 3:00pm in 532 Rowland Hall).
Wednesday, October 4
Combinations continued, multinomial coefficients (Sections 1.1-1.5).
Homework 2 (due October 12):
From Chapter 1: 23, 24, 27, Theoretical Exercises 5, 13.
From Chapter 2: 1, 2, 3, 5, 6, 7.
Friday, October 6
Number of integer solutions (1.6). Sample space and events. Operations on events (2.1-2.2).
Monday, October 9
Axioms of probability. Inclusion-Exclusion Principle (2.4 up to Example 4a).
Wednesday, October 11
Inclusion-Exclusion Principle continued. Sample spaces having equally likely outcomes (2.5 begins).
Friday, October 13
Generalized Inclusion-Exclusion Principle (Proposition 4.4). The Matching Problem (Example 5m).
Homework 3 (due October 19) from Chapter 2: 8, 9, 10, 12, 14, 17, 21, 25, 28, 29(a), 32, 37, 39, 41.
Monday, October 16
Conditional probabilities. The Law of Total Probability (3.1-3.2).
Wednesday, October 18
The Best Prize Problem (Chapter 7, Example 5k). Bayes Formula (3.3).
Friday, October 20
Bayes Formula cont. Prior and posterior probabilities (Bayesian statistics).
Bayesian spam filtering (Bayesian machine learning). Three Prisoners Problem.
Homework 4 (due October 26) from Chapter 3: 1, 2, 4, 7, 12, 15, 16, 19, 20, 21, 23, 26, 33, 37, 51.
Monday, October 23
Independent events (3.4). Computing probabilities by conditioning. Simple random walk (Example 4m).
Wednesday, October 25
Midterm Exam 1,
solutions.
Friday, October 27
Independence cont. Finding your birthmate problem. Random variables (4.1). Discrete random variables. Probability mass function (4.2).
Homework 5 (due November 2) from Chapter 3: 55, 57, 58, 62, 64, 66, 73, 81, 91; from Chapter 4: 1, 4, 5, 6, 14.
Monday, October 30
Cumulative distribution function (cdf).
Wednesday, November 1
Expected value (4.3). Examples: lottery; group testing. Expected value of a function of a random variable (4.4).
Friday, November 3
Variance (4.5). The matching problem (expectation and variance). Analysis of Quicksort (Chapter 7, Example 2m).
Homework 6 (due November 9) from Chapter 4: 17, 18, 19, 20, 21, 22(a), 23, 26, 30, 35, 36, 37, 38.
Monday, November 6
Bernoulli and binomial distributions (4.6).
Wednesday, November 8
Poisson distribution. Poisson approximation of the Binomial distribution (4.7).
People vs. Collins.
Homework 7 (due November 16) from Chapter 4: 39, 40, 41, 42, 43, 45, 49, 51, 52, 53, 55, 56 (use Poisson approximation), 57, 60.
Monday, November 13
Computing expectations by conditioning: law ot total expectation (7.5). Geometric distribution (4.8.1). Coupon collector's problem (Ch.7 Ex. 2i).
Wednesday, November 15
Negative binomial (4.8.2), the problem of points, Banach match problem. Hypergeometric distribution (4.8.3).
Friday, November 17
Continuous distributions, pdf (5.1). Uniform distribution (5.3).
Monday, November 20
Midterm Exam 2,
solutions.
The exam covers the material that we covered in class during October 23 (Section 3.4) through November 8 (Section 4.7).
Wednesday, November 22
Transformations of random variables (5.7). Benford's law.
Homework 8 (due November 30) from Chapter 7: 6, 7, 8, 11, 33, 53, 58; from Chapter 5: 1, 2, 4, 11, 13, 37, 40.
Monday, November 27
Expectation and variance of continuous distributions (5.2)
Wednesday, November 29
Normal distribution (5.4).
Friday, December 1
Normal distribution cont. Normal approximation to binomial distribution (5.4.1).
Homework 9 (due December 7) from Chapter 5: 6, 7, 14, 15, 16, 17, 18, 19, 20, 22, 23, 25, 26, 31(a), 38.
Monday, November 4
Normal approximation cont. (5.4.1).
Wednesday, November 6
Exponential distribution (5.5).
Homework 10 (will not be collected) from Chapter 5: 32, 33, 34, 39.
Friday, December 8
Review.
Wednesday, December 13, 4:00-6:00 pm
Final Exam.