STAT2911: Probability & Statistical Models (Advanced)
Semester 1, 2012

Announcements

• Make sure you gain access to the linked page

Staff

• Lectures and Tutorials: Uri Keich
• Computer Lab: Emi Tanaka

Schedule

• Lectures (Carslaw 351): Mon 11am, Tue 11am, Wed 1pm

Grading Structure and Schedule

• One or two quizzes held in the lecture (5%)
• Two assignments (5%)
• Computer work handed in weekly (10%)
• A one-hour computer exam (open book) held instead of the very last lecture (10%)
• A two hour final examination (70%)
• A solved problem set is due at the start of each tutorial. This work will be partially graded and these grades will be a major component in the evaluation of any special consideration request.

Textbook

• Rice J.A. Mathematical Statisics and Data Analysis 3rd Edition.

References

• Feller, W. An Introduction to Probability Theory and its Applications Third edition, Volume 1.
• Information for both the the R computing system and the process() utility for preparing computer exercise reports.
• The R guide by Jason Owen.
• There are many user-contributed manuals/guides for R on the R website including two R "Reference Cards", one which is one page and another which is four pages.

Learning Outcome

• Probability Axioms; independence; conditional probability;
• Discrete distributions and random variables;
• Expectation; functions of rv; variance; Chebychev's inequality;
• Sums of independent discrete rv; Bernoulli variables; Binomial distribution;
• Geometric and negative binomial distributions; Poisson distribution;
• Weak law of large numbers; Poisson limit of binomial;
• hypergeometric distribution; multivariate distributions; multinomial distribution; simulation of discrete rv;
• Estimation of parameters using Method of Moments;
• Estimation of parameters using Maximum Likelihood;
• Unbiased estimator; Mean Square Error; Comparing estimators; parametric bootstrap for estimates
• The delta method;
• Random sums; Conditional expectation;
• Continuous distributions and random variables: uniform, exponential, gamma, normal, beta, Cauchy; Chi^2; t; F;
• Functions of random variables (continuous case);
• Independent random variables; Sums and quotients of independent random variables;
• Transformation of bivariate RVs;
• Expectation, variance and covariance (continuous case);
• Bivariate normal distribution;
• Simulations;
• Order Statistics;
• Estimation of parameters using Method of Moments and Maximum Likelihood (continuous case);
• Q-Q plots; probability plots;
• Random sums and Conditional expectation (continuous case);
• Central limit theorem and applications;
• Interval estimation; CI for mean of normal; CI for variance;
• CI for proportions; bootstrap CI
• Distributions related to the normal; Sampling distributions of statistics from normal distributions;