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