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Module details

IA116-3-FY: INTRODUCTION TO PROBABILITY AND STATISTICAL METHODS

Year: 2014/15
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: No

Staff
Contact details: jpsumm (Non essex users should add @essex.ac.uk to create the full email address)

 Module is taught during the following terms Autumn Spring Summer

Module Description

This module introduces students to basic ideas of probability including combinatorial analysis, rules of probability, conditional probability, statistical independence and probability distributions. Data collection and descriptive statistics for data handling are introduced and provide insight into theoretical concepts of probability. Students are taught how the R software package can be used to generate random variables and to construct diagrams to summarise data.

The aims of the module are:

- To ensure that students from a wide range of educational backgrounds have a broad understanding of basic statistical skills

- To give students the ability to present data clearly and unambiguously to an audience with no specialist knowledge of statistics

- To give students an understanding and ability to calculate basic statistical measures

- To provide students with an introduction to probability theory

- To introduce students to a range of tools for calculating probabilities

- To provide knowledge of various models of probability distributions and the requirements underlying the models

Learning outcomes

On successful completion of the module a student will demonstrate the ability to:

- collect data and clearly present data in tables and diagrammatically

- calculate and interpret simple summary statistics

- use R to undertake some simple data analysis

- use probability rules to calculate the probability of simple and joint events and conditional probabilities

- understand and calculate probabilities from discrete probability distributions including the Binomial and Poisson probability distributions

- understand and calculate probabilities from continuous probability distributions including the Normal distribution

- understand the central limit theorem and approximations to probability distribution functions.

Syllabus

1. Descriptive statistics: data collection and summary; stem and leaf plots, box plots and histograms; measures of location and dispersion; transformations.

2. Probability: relative frequencies and probability as a limit; simple and joint events; Venn diagrams, union and intersection of events; mutually exclusive events; addition rule of probability.

3. Conditional probability: statistical independence; multiplication rule of probability; total probability theorem; Bayes theorem.

4. Discrete probability distributions: discrete random variables; expected values and variance; Bernoulli distribution and Binomial distribution; Poisson distribution and approximation to the binomial.

5. Continuous probability distributions: density function as limit of histograms; properties of probability density functions; cumulative distribution functions; Uniform and Exponential probability distributions; change of variables formula.

6. Normal probability distribution: standardising normal variables; using tables to calculate normal variables; central limit theorem; adding normal variables

Learning & Teaching Methods

Students are required to attend a one-hour lecture and a two-hour class per week. An additional one hour class per week may be offered as extra support to students.

Assessment

40 per cent Coursework Mark, 60 per cent Exam Mark

Coursework is comprised of:

1st in-class test in week 9 (25%). Feedback provided in week 12.

2nd in-class test n week 20 (75%). Feedback provided in week 23.

Exam Duration and Period

2:00 hour exam during Summer Examination period.

Learning & Teaching Methods

Students are required to attend a one-hour lecture and a two-hour class per week.

Assessment

40 per cent Coursework Mark, 60 per cent Exam Mark

Exam Duration and Period

2:00 hour exam during Summer Examination period.

Bibliography

• Crawford, J. & J. Chamber (2001) A Concise Course in Advanced Level Statistics with Worked Examples, 4th ed. Nelson Thornes.
• Newbold, P., W. L. Carlson & B. Thorn (2006) Statistics for Business & Economics, 6th ed. Pearson Education.
• Triola, M. F. (2007) Elementary Statistics Using Excel, 3rd ed. Pearson Education.