Math 312 – Probability and Statistics 2,  Winter 2013

      


Instructor: Anatolii Grinshpan
Office hours:  TR 12-1, Korman 247, or by appointment, Korman 253.

Course information   Schedule   Academic Calendar       Some links: Tutoring center

Jan. 8.  Introduction to the course. The bridge-crossing problem.

Jan. 10. Simple random sampling. Examples. The expectation and variance of the sample mean.

Reading: pages 199-207 of the handout. Problems (due Jan 17).

 

Jan. 15. Properties of covariance. Sampling without replacement: a lemma on covariance, variance of the sample mean .

Jan. 17. Chebyshev’s inequality. The law of large numbers. The central limit theorem

Reading: pages 207-210, 177-180 of the handouts. Problems (due Jan 24). Problems on CLT.

 

Jan. 22. Bernoulli’s theorem. Standard Gaussian. Proof of the central limit theorem. Normal approximation to the binomial distribution.

Jan. 24. Point estimation. Waiting times. Estimation of the population variance.

Reading: pages 181-188 (examples), 210-214 of the handouts. Problems (due Jan 31).

 

Jan. 29. The method of moments. The method of maximum likelihood.

Jan. 31. Confidence intervals for population mean (simple random sampling).

Reading: pages 240 – 252 of D, point estimation, pages 214 – 220 of R.

 

Feb. 4. Questions session:  6 - 7+ PM, CAT 76.

 

Feb. 5. Midterm 1.

Feb. 7. Midterm solutions.

Reading: confidence intervals. Problems (due Feb 14).

 

Feb. 12. Student’s t distribution. (t calculator) Buffon’s needle. One-sided confidence intervals.

Feb. 14. Chi-square distribution. (chi calculator) Confidence intervals for standard error. Hypothesis testing.

Reading: pages 192-198 of R (facts about t and chi), 301-308 of D. Problems (due Feb 21).

 

Feb. 19. Shortest interval for standard error. Hypothesis testing.

Feb. 21. Likelihood ratio. Neyman – Pearson paradigm.

Reading: pages 310-327 of D.  Problems (due Mar 4).

 

Feb. 26. Tests for mean, variance, and proportion. Goodness-of-fit test.

Feb. 28. The duality of confidence intervals and hypothesis tests. Fisher vs Mendel.

Reading: Stein’s paradox, lottery code. Sample test.

 

Mar. 4. Questions session:  6 - 7+ PM, Lebow 135.

 

Mar. 5. Midterm 2.

Mar. 7. No class.

 

Mar. 12. Pearson’s chi-square test. Least squares fit.

Mar. 14. Perpendicular regression. Regression coefficients: expectation and variance.

Reading: pages 542-563 of R. Problems.

 

Mar. 22. Questions session: 3-4+, Stratton 101.

 

Mar. 23. Final exam: 8-10 AM, Curtis 457.