24 lectures; 24 hours of tutorial and practice classes plus practical work;
second term; 3 points.
Condition: Students may not gain credit for this course and for Statistics 102.
SYLLABUS A brief outline of the probability and distribution theory re- quired for application in the course. Binomial, Poisson, negative binomial, normal, uniform distributions. Index of dispersion. Central limit theorem.
Random sampling. Analysis of data: mean, median, variance. Introduction to inference: the likelihood function, maximum likelihood and moment estimates, point and interval estimation. Tests of hypotheses, with par- ticular reference to distribution free methods: sign, permutation, Wil- coxon two sample, Wilcoxon signed-rank tests.
181
Books
Preliminary reading:
As for Statistics 101 to 103.
Students who have not studied probability at HSC level are advised to read:
Watson R K Elementary Probability and Some Statistics, VABA EXAMINATION 2-hour terminal examination. Candidates must also satis- factorily complete the practical work.
121 INTRODUCTORY STATISTICS
24 lectures; 24 hours of tutorial and practice classes plus practical work;
summer course (February); 3 points.
Condition: Students may not gain credit for this course and for Statistics 102 or 112.
SYLLABUS As for Statistics 112.
EXAMINATION 2-hour examination before the start of first term. Candi- dates must also complete practical work.
112 APPLIED STATISTICS
24 lectures; 24 hours of tutorial and practice classes plus practical work;
third term; 3 points.
Condition: Students may not gain credit for this course and for Statistics 103.
Prerequisite: Statistics 112.
SYLLABUS Student's t test with applications. Paired comparisons and the principles of design. Correlation, rank correlation, fitting straight lines, linear regression models, prediction and testing. Tests based on the chi-squared distribution: Goodness of fit, contingency tables; graphi- cal methods. F distribution and one way analysis of variance. Sample surveys: random, stratified sampling, optimal allocation of samples.
EXAMINATION 2-hour terminal examination. Candidates must also satis- factorily complete the practical work.
200 LEVEL
The Standard Statistics second year course consists of the units 201, 202 and 203. This course is intended to give a basic understanding of Statistics. Mathematics 131 or 171 is a prerequisite, and it is recom- mended that students taking this course should be studying Mathematics at 200 level concurrently or have taken it previously. Students who have not previously taken Statistics 112 or 122 are recommended to consult the departmental notice-board concerning preliminary reading. Details of prescribed and recommended books may be obtained from the Depart- ment of Statistics.
Students with an interest in Operations Research should also take 263.
201 PROBABILITY
24 lectures and 24 tutorial/practice class hours plus a practical project;
first term; 5 points.
Prerequisite: Mathematics 131 or 171.
SYLLABUS Elementary probability concepts. Random variables and de- scriptions of their probability distributions. Expectation. Generating functions. Applications to Bernoulli trials, Poisson process and random sampling. Simple Markov chains. Standard probability distributions, Including hypergeometris, binomial, Poisson, negative binomial, normal, gamma and beta distributions, and some of their applications. Sampling theory: order statistics; t. X2 and F distributions. The law of large num- bers and the central limit theorem.
EXAMINATION 2-hour terminal examination, together with assessment of practical work and project.
202 STATISTICAL INFERENCE
24 lectures and 24 tutorial/practice class hours plus a practical project;
second term; 5 points.
Prerequisites: Statistics 201; Statistics 112 (or 122) is strongly recom- mended.
SYLLABUS Estimation of parameters of probability distributions; de- sirable properties of estimators—consistency, unbiasedness and efficiency.
Methods of estimation. Minimum variance bound for unbiased estimators.
Properties of maximum likelihood estimators. Confidence intervals for parameters. Testing of hypotheses concerning parameters; critical region, size and power of tests. Likelihood ratio tests. Particular reference is made to the case of sampling on a normal distribution, for which the t, X2 and F distributions are required. Details of some commonly occur- ring statistical tests including contingency tables, goodness of fit tests,
one-way analysis of variance, and some distribution free tests. An Intro- duction to Sequential Analysis, Sample Surveys and Decision Theory.
EXAMINATION 2-hour terminal examination, together with assessment of practical work and project.
203 STATISTICAL ANALYSIS
24 lectures and 24 tutorial/practice class hours plus a practical project;
third term; 5 points.
Prerequisite: Statistics 202.
SYLLABUS Linear regression and the method of least squares. Correlation:
bivariate and multivariate normal distributions. The theory and the appli- cations of the general linear model—with particular reference to regres- sion problems including multiple and polynomial regression; to one-way and two-way analysis of variance; and to the analysis of statistical experiments such as randomization and formation of blocks. The study of some standard experimental designs, including randomized block, balanced incomplete block and 2k factorial experiments.
BOOKS
List of prescribed textbooks obtainable from the department.
EXAMINATION 2-hour terminal examination, together with assessment of practical work and project.
183
263 FORECASTING
16 lectures and 16 tutorial/practice class hours plus a practical project;
third term; 4 points.
Prerequisite: An approved basic course in mathematical statistics at least of the standard of Statistics 101-103 or Statistics 112-113.
SYLLABUS Mathematical aids to trend estimation and forecasting. The forecasting of traffic matrices. Simple analysis of time series into sea- sonal fluctuation, trend and disturbance components. Optimum choice of forecasting methods.
EXAMINATION 2-hour terminal examination, together with assessment of practical work and project.
300 LEVEL
The Statistics units in third year develop the material of Statistics 200 level and introduce new probabilistic and statistical areas. Students may take any selection of units, subject to prerequisites in Statistics and Mathematics. There are streams in probability and stochastic processes (301, 321, 322), inference (311, 313, 314 plus 315, 317) and operations research (361 or 301 ± 311, 362, 363, 364).
Students majoring in Statistics should take at least half their third year course from Statistics 300 level units; some units from Mathematics, Computer Science or other Science disciplines should also be taken.
Other students may take individual units.
Students intending to study fourth year honours in Statistics should take at least Statistics 301, 311, 313, 321 and 331, together with some advanced level Mathematics 300 level units.
301 PROBABILITY
24 lectures and 18 tutorial/practice class hours; first term; 5 points.
Prerequisites: Statistics 201; Mathematics 271 (or 231) and 273 (or 233).
Conditions: Students may not gain credit for this course and for Statistics 361.
SYLLABUS Basic methods in probability and distribution theory for dis- crete and continuous sample spaces. Distribution functions, generating functions, characteristic functions. Convergence and limit laws. Detailed treatment of various special distributions end their inter-relations.
EXAMINATION 3-hour terminal examination, together with assessment of practical work.
BOOKS
Prescribed textbooks:
Heathcote C R Probability Elements of Mathematical Theory, Unwin Feller W An Introduction to Probability Theory Vols I & II, Wiley 184