Math 311 – Probability and Statistics, Spring 2016

laplace.png    

Instructor: Anatolii Grinshpan

Office hours:  Tue 12-2 & Th 1-2, Korman 249

Course information   Grinstead & Snell    History    Tutoring center

 


Mar 28.  Introduction to the course.  Division of stakes. Finite probability framework. Venn diagramsMonotonicityExample.
Mar 30.  De Méré’s bets. Uniform distribution. Properties of probability. Tree diagrams. Odds. Countable probability model.

Reading: 1.1, 1.2Problems. d’Alembert’s misstep.

 

Apr   4.  Quiz 1 (Chapter 1). Continuous probability model. Continuous uniform distribution. Monte Carlo procedure.

Apr   6.  Buffon’s needle. Bertrand’s paradox. The density function. The cumulative distribution function. Examples.

Reading:  2.1, 2.2Problems.

 

Apr 11.  Quiz 2 (Chapter 2). Combinatorics. Counting principle. The birthday problem.

Apr 13.  Permutations and combinations. Bernoulli trials. Binomial distribution. Inclusion-exclusionExample.

Reading: 3.1, 3.2. Problems.

 

Apr 18. Quiz 3 (Chapter 3). Binomial odds ratios. Conditional probability (discrete setting). Reverse tree diagrams. Reading: 4.1.

Apr 19. Questions session: Lebow 135,  5:10-6:30 PM.

Apr 20. Midterm 1 (1-3, 4.1).

 

Apr 25. Monty Hall problem.  Bayes’ formula. Independence of events. Joint, marginal, and conditional probability mass functions. 

Apr 27. Independence of random variables. Continuous conditional probability. Mass vs density.

Reading: 4.1, 4.2. Problems.

 

May 2.  Quiz 4 (Chapter 4). Joint, marginal, and conditional probability density functions. Example.

May 4.  Independence of continuous variables. Some common probability mass and density functions.  Cauchy density.

Reading: 5.1, 5.2. Problems.

 

May 9.   Quiz 5 (Chapter 5). Random coin. Expected value and variance (discrete setting).

May 11. Expected value and variance (continuous setting).

Reading: 6.1-6.3. Problems.

 

May 16. Quiz 6 (Chapter 6).  Convolution. Binomial as a convolution. Sum of binomials. Reading: 7.1.

May 17. Questions session: Curtis 250A, 5-6 PM.

May 18. Midterm 2 (4.2, 5, 6, 7.1).

 

May  23. Sums of continuous variables: uniform, normal. Reading: Section 7.2.

May  25. Chebyshev’s inequality.  The Law of Large Numbers.

Reading: 8.1, 8.2. Problems.

 

June 1.   Quiz 7 (Chapter 8). The Central Limit Theorem. De Moivre – Laplace. Spike plots. Local Limit Theorem. Reading: 9.1-9.3.

June 3.   Office hours 2-4, Korman 249.

June 6.   Questions session.

June 7.   Final exam (all lectures): Lebow 135, 8-10AM