Class Syllabus for Math 311
Text: Probability, by Jim Pitman
Professor Verzani, Fall 1998

Homework will be collected periodically. The exact questions will be announced in class. The questions within the [] are optional.

Chapter 1. Elements of Probability
1.1: Equally likely outcomes HW: pgs. 9-10:1,3,4,7
1.2: Interpretations HW: pgs. 18: 1
1.3: Distributions HW: pgs. 30-32: 2,3,5,8,10 [11]
Statistics Handout: Empirical distributions, histograms etc.
1.4: Independence HW: pgs. 45-46: 1,3,4,5,6,8 [11,12]
1.5: Bayes’ rule HW: pgs. 53-55: 1,2,3,5 [7]
1.6: Sequences of Events HW: pgs. 70-71: 1,2,3,7,8

Chapter 2. Repeated Trials and sampling
2.1: The Binomial Distribution HW: pgs. 90-92: 1,3,5,7,11 [14]
2.2: Normal approximation to binomial HW: pgs. 108-110: 1,2,5,9,11,12,15
2.3: skip
2.4: Poisson approximation to the binomial HW: pgs. 121-122: 3,5,9
2.5: Random sampling HW: pgs. 127-129: 2,3,6,9,12

Chapter 3. Random Variables
3.1 Introduction HW: pgs. 158-161: 1,2,3,8,13,15 [10,16,18,23]
3.2: Expectation HW: pgs. 182-184: 1,3,4,6,8,13 a,b [13cdef,15,17]
3.3: Standard Deviation HW: pgs. 202-207: 1,2,7,13,19 [23,26,30]
3.4: Discrete Distributions HW: pgs. 217-221: 1,2,3,7,9 [13,15,19,24]
3.5: The Poisson Distribution HW: pgs. 233-236: 2,4,5,8,14 [13,18]
3.6: skip

Topics in Statistics. Statistics Handouts on.
1. Estimation of parameters, confidence intervals.
2. Hypothesis testing. 3. Loss functions.

Chapter 4. Continuous Distributions
4.1: Probability densities HW: pgs. 275-277: 1,2,3,8,9
4.2: Exponential Distribution HW: pgs. 293-295: 2,3,4 abc,5,9,
4.3: skip
4.4: Change of variable HW: pgs. 309-310: 1,3,4,6,8
4.5: Cumulative distribution functions HW: pgs. 323-324: 1,2,4,5,6 a,b,c

Chapter 5. Continuous joint distributions
5.1: Uniform Distribution HW: pgs. 344-345: 1,3,5,7,8
5.2: densities HW: pgs. 354-356: 1,5,6,7,9 [13,21]
5.3: Independent Normal variables HW: pgs.366-370: 1 abcd,7,9,12
5.4: skip

Chapter 6. Dependence
6.4: Covariance and Correlation HW: pgs. 445-448: 1,3,8,10,18