Math 312 – Probability and Statistics 2,  Winter 2015


Instructor: Anatolii Grinshpan
Office hours:  T 12-1 & R 12-2, Korman 249.

Course information    Academic Calendar    Tutoring center    John Rice    R project    Philip Stark

Jan 6.   Introduction. Measures of location and measures of dispersion. Simple random sampling.

Jan 8.   Quantiles. Shape parameters. Empirical frequency function. Histograms, stem-and-leaf plots, QQ plots, boxplots.

Reading: Ch. 10. Problems: due January 15.


Jan 13. Sampling with and without replacement. The distribution of the sample mean. Variance of the sample mean. Example.

Jan 15. Order statistics. Covariance calculation. Sample variance. Lagrange identity. Bessel correction.

Reading: Ch. 7. Problems: due January 22.


Jan 20. The distribution of the sample variance. Sampling from normal distribution. Types of sampling.

Jan 22. Confidence intervals for the population mean. Point estimation of parameters. The method of moments. Waiting times.

Reading: Ch. 7, 8. Problems: due January 29.


Jan 27. Waiting times. The method of maximum likelihood. Capture-recapture.

Jan 29. Sampling from multinomial distribution. Examples of parameter estimation.

Reading: Ch. 8. Problems.


Feb 2.  Questions session 1-2 PM (Korman 207).

Feb 3.  Midterm 1 (lectures of Jan 6 – Jan 29).

Feb 5.  Hypothesis testing. Example.

Reading: Ch. 9. Problems: due February 12.


Feb 10. Likelihood ratio test. Chi-square distribution (chi calculator). Student’s t-distribution (t calculator).

Feb 12. Hypothesis testing: test statistic, null distribution, power curve, z-tests and t-tests.

Reading: Ch. 8, 9. Problems: due February 19.


Feb 17. Bayes vs Neyman-Pearson. P-values. Confidence intervals and hypothesis tests. Pearson’s theorem.

Feb 19. Chi-square test. The likelihood ratio test for the mean of a normal distribution.

Reading: Ch. 9. Problems: due February 26.


Feb 24. The likelihood ratio test for the mean of a normal distribution.

Feb 26. Dance of the p-values. The generalized likelihood ratio. Multinomial context.

Reading: Ch. 9. Problems.


Mar 2.  Questions session 11-Noon (Korman 207).

Mar  3. Midterm 2 (lectures of Feb 5 – Feb 26).

Mar 5.  Comparing two samples: z and t tests, paired tests.

Reading: Ch. 11. Problems: due March 12.


Mar 10. Analysis of variance. (F calculator).

Mar 12. Linear least squares. Simple model.

Reading: Ch. 12, 14. Problems.


Mar 17. Questions session 1-2+ PM, Curtis 344.

Mar 19. Final exam (all lectures), 8-10 AM, Curtis 344.