STAT2911: Probability & Statistical Models (Advanced)
Semester 1, 2013

Announcements

• The second and last assignment is now posted. It is due at the start of the lecture on Wednesday May 29.
• I will join the strike this Tuesday. Find out here why. In practical terms it means that we will not have a class nor tutorial this Tuesday 14/5. I apologize for compromising your learning experience. I can only assure you that I am not taking this decision lightly and that it carries a substantial financial consequence for me.
• The class representative for this unit is Tom Diep (tdie1688). Please let me know if you would like to join Tom in meeting with school representatives this week, or more likely the next one.
• Class notes are available (updated 22/5/13)
• Tutorial sets are available (updated 22/5/13)
• Computer lab notes are available (updated 19/5/13)

Staff

• Lectures and Tutorials: Uri Keich
• Computer Lab: Chong You

Schedule

• Lectures: Mon 11am (Carslaw 350), Tue 11am (Carslaw 351), Wed 1pm (Carslaw 351)
• Tutorials: Tue 1pm (Carslaw 451) OR Wed 2pm (Eastern Av 310)
• Computer Lab: Wed 3pm (Carslaw 729) OR Wed 4pm (Carslaw 729)
• Office Hour (Carslaw 821): Mon 5pm

Grading Structure and Schedule

• One quiz held in the lecture on 16/4/2013 (5%)
• Two assignments (5%)
• Computer work handed in weekly (10%)
• A one-hour computer exam (open book) held in the last week (10%)
• A two hour final examination (70%) to be held on Mon 24 Jun 2013 09:00AM
• 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
• There are many user-contributed manuals/guides for R on the R website

Learning Outcome

The students will gain knowledge of the following subjects:
• 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;