# Module Information

#### Course Delivery

Delivery Type | Delivery length / details |
---|---|

Lecture | 22 Hours. (22 x 1 hour lectures) |

Seminars / Tutorials | 4 Hours. (4 x 1-hour tutorials) |

#### Assessment

Assessment Type | Assessment length / details | Proportion |
---|---|---|

Semester Exam | 2 Hours (written examination) | 80% |

Semester Assessment | (coursework) | 20% |

Supplementary Exam | 2 Hours (written examination) | 100% |

### Learning Outcomes

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 statistical tests and confidence intervals;

9. construct and carry out simple tests and confidence intervals;

10.use relevant statistical tables.

### Brief description

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.

### Aims

To introduce the subject of Statistics to mathematics students.

### Content

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.

### Reading List

**Recommended Text**

Freund, John E. (c2004.) John E. Freund's mathematical statistics with applications /John E. Freund. Prentice Hall Primo search Hogg, Robert V. (c2006.) Probability and statistical inference /Robert V. Hogg, Elliot A. Tanis. Prentice Hall Primo search

**Supplementary Text**

D D Wackerley, W Mendenhall & R L Scheaffer (2002) Mathematical Statistics with Applications 6th Duxbury. Primo search Strait, Peggy Tang. (c1989.) A first course in probability and statistics with applications /Peggy Tang Strait. Harcourt Brace Primo search Weiss, N. A. (c2006.) A course in probability /Neil A. Weiss, with contributions from Paul T. Holmes, Michael Hardy. Pearson Addison Wesley Primo search

### Notes

This module is at CQFW Level 4