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.
Course information Academic
Some links: Tutoring center
Jan 7. Introduction. First
examples: average crossing time, Benford’s law,
capture/recapture method (Rice, page 13).
9. Simple random
sampling. Properties of covariance (Rice, 138-46). Example.
Population mean and variance.
Rice, pages 199-205. Problems: due January
14. Sample mean vs population mean. The expected value of the
sample mean. Covariance lemma. Variance of the sample mean.
16. Homework discussion. Empirical frequency (Rice, 378-80). Population median.
Rice, pages 206-210. Problems: due January
The distribution of the empirical frequency (Rice, 379-80). Splitting the data. An example on waiting times.
Homework discussion. Chebyshev’s inequality
(Rice, 121, 133-4). Bernoulli’s theorem.
The law of large numbers (Rice, 177-80).
due January 30.
Normal distribution. de Moivre – Laplace. Illustration. Example. Galton board.
Moment-generating functions (Rice, 155-61).
The central limit theorem (Rice, 181-88). Estimation
of variance (Rice 210-14). More on
due February 6 (optional).
Feb 3. Questions session 10-11:30, Korman 245.
Feb 4. Exam 1 (lectures of January 7 - 30).
Homework discussion. Special properties of normal distribution. Confidence intervals (Rice, 214-20).
due February 18.
Exam discussion. Stratified random sampling (Rice, 227-39).
temperature. Daily temperature. Monthly
Lagrange identity. Stratified sampling. Ratio
estimation (Rice, 220-227).
Confidence intervals for the ratio and ratio estimate. Reading: Stein averaging
(optional). One-sided confidence intervals.
due February 25.