# Math 312 – Probability and Statistics 2,  Winter 2014

Instructor: Anatolii Grinshpan
Office hours:  TR 12-1 & W 1-2, Korman 249, or by appointment, Korman 253.

Jan 7.    Introduction. First examples: average crossing time, Benford’s law, capture/recapture method (Rice, page 13).

Jan 9.    Simple random sampling. Properties of covariance (Rice, 138-46). Example. Population mean and variance.

Reading: Rice, pages 199-205. Problems: due January 16.

Jan 14.  Sample mean vs population mean. The expected value of the sample mean. Covariance lemma. Variance of the sample mean.

Jan 16.  Homework discussion. Empirical frequency (Rice, 378-80). Population median.

Reading: Rice, pages 206-210. Problems: due January 23.

Jan 21. The distribution of the empirical frequency (Rice, 379-80). Splitting the data. An example on waiting times.

Jan 23. Homework discussion. Chebyshev’s inequality (Rice, 121, 133-4). Bernoulli’s theorem. The law of large numbers (Rice, 177-80).

Problems: due January 30.

Jan 28. Normal distribution. de Moivre – Laplace. Illustration. Example. Galton board. Moment-generating functions (Rice, 155-61).

Jan 30. The central limit theorem (Rice, 181-88). Estimation of variance (Rice 210-14). More on variance estimation.

Problems: due February 6 (optional).

Feb 3. Questions session 10-11:30, Korman 245.

Feb 4. Exam 1 (lectures of January 7 - 30).

Feb 6. Homework discussion. Special properties of normal distribution. Confidence intervals (Rice, 214-20).

Problems: due February 18.

Feb 11. Exam discussion. Stratified random sampling (Rice, 227-39).

Feb 18. Lagrange identity. Stratified sampling. Ratio estimation (Rice, 220-227).

Feb 20. Confidence intervals for the ratio and ratio estimate.  Reading: Stein averaging (optional). One-sided confidence intervals.

Problems: due February 25.