Course Outline


SMS 3200 Probability and Statistics II


To equip students with statistical programming and simulations techniques.

Expected Learning Outcomes:

At the end of the course, students should be able to:

1. Derive point and interval estimates.

2. Compute variance estimates.

3. Make basic statistical inference.

4. Develop an algorithm that computes statistical moments.

5. Understand basic simulation procedures.

6. Generate random numbers and random variates.

7. Apply Monte-Carlo methods to real life.

Course content:

• Basic knowledge of high level programming languages such as Ms Excel, C++, S-plus and R, MATLAB .

• Computer arithmetic. ; statistical graphics, sampling variability.

• Point and confidence interval estimation; estimating a mean, estimating a proportion, estimating a variance, estimating a variance ratio, bootstrap estimation.

• Hypothesis testing.

• Algorithm for mean and standard deviation.

• Error analysis.

• Basic simulation procedures, Pseudo random number generators; properties of random number generators. Techniques for generating random numbers. Generation of random variates:

• Discrete and continuous distributions. Monte Carlo simulation. Application of monte-carlo simulation; random walk, integrals, area of irregular shape. waiting lines. flow charts and algorithms of simulation models.

• Parameter estimation. use of simulation language.

Mode of delivery

2 hour lecture and 1 hour tutorial per week, Discussions and Research

Instruction materials/equipment

Board, White board and marker pens, Computer laboratory Projector and computer accessories, handouts

Course Assessment

• Continuous Assessment Tests 30%,

• Written end of semester examination 70% ,

• Total mark 100%

Core references

1. Robert J. Schalkoff. Programming Languages And Methodologies. Jones & Bartlett Publishers; 2006.

Recommended references:

1. Simon Bennett, Steve McRobb , Ray Farmer. Object-Oriented Systems Analysis and Design Using UML (Paperback) Object-Oriented Systems Analysis and Design Using UML. 3rd Edition. McGraw-Hill. 2006

2. Crawley. Statistics: An Introduction Using R. John Wiley & Sons, 2005

3. H.J Larson. Introduction to Probability Theory and Statistical Inference(Probability and Mathematical Statistics). 3rd ed., Wiley, 1982