|| MA11310 |
|| STATISTICS |
|| 2007/2008 |
|| Dr John A Lane |
|| Semester 2 |
|| Mrs Glenda Roberts, Gareth D E Lanagan, Dr John A Lane, Mr Alan Jones |
|| MA10310 |
| Course delivery
|| Lecture || 22 Hours. (22 x 1 hour lectures) |
|| Seminars / Tutorials || 5 Hours. (5 x 1 hour tutorials) |
|Assessment Type||Assessment Length/Details||Proportion|
|Semester Exam||2 Hours (written examination) ||100%|
|Supplementary Assessment||2 Hours (written examination) ||100%|
On completion of this module, a student should be able to:
1. describe the notion of covariance;
2. calculate means and variances of linear combinations of random variables;
3. identify a probability distribution appropriate to a given situation;
4. describe modelling in terms of Bernoulli trials and of random events;
5. manipulate distributions to obtain moments and to sketch curves;
6. assess a given value in relation to the scale of a given probability distribution;
7. estimate means and proportions from data;
8. explain the use of a statistical test;
9. construct and carry out simple tests.
10. use relevant statistical tables
This module aims to develop common probability models, applicable to a variety of situations and to illustrate their use in statistical inference. It also includes an introduction to the theory of estimation.
To introduce the subject of Statistics to mathematics students.
1. THE INFERENCE PROBLEM: The difference between probability and statistical inference. Assessing 'typical' values from a distribution. The idea of a statistic. Estimates and estimators. Accuracy and precision. Bias, sampling, variance and mean squared error. Comparison of estimators.
2. PROBABILISTIC (STOCHASTIC) MODELLING (INCLUDING EXAMPLES OF INFERENCE): Bernoulli trials and distributions based on them (Geometric, Binomial). Opinion polls. The ideas of covariance and correlation. Variances of linear combinations of random variables. Modelling random events. The Poisson and exponential distributions. Normality and the Central Limit Theorem. The Weak Law of Large Numbers.
3. INFERENCE: Sampling mean, sampling variance and standard deviation of a sample total and a sample average. Statistical testing. Tail areas. p-values. Examples of simple tests. The notion of a confidence interval.
** Recommended Text
Freund, John E. (c2004.) John E. Freund's mathematical statistics with applications /John E. Freund.
Prentice Hall 0131246461
Hogg, Robert V. (c2006.) Probability and statistical inference /Robert V. Hogg, Elliot A. Tanis.
Prentice Hall 0131464132
** Supplementary Text
D D Wackerley, W Mendenhall & R L Scheaffer (2002) Mathematical Statistics with Applications
6th. Duxbury. 0534377416
Strait, Peggy Tang. (c1989.) A first course in probability and statistics with applications /Peggy Tang Strait.
Harcourt Brace 0155275232
Weiss, N. A. (c2006.) A course in probability /Neil A. Weiss, with contributions from Paul T. Holmes, Michael Hardy.
Pearson Addison Wesley 032118954X
This module is at CQFW Level 4