2008/09 Undergraduate Module Catalogue
MATH1715 Introduction to Probability
10 creditsClass Size: 300
Module manager: Dr L.V. Bogachev
Email: bogachev@maths.leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2008/09
Pre-requisite qualifications
A-level Mathematics (Algebra and Calculus - you don't need to have done any A-level Statistics modules).This module is approved as an Elective
Module summary
"Probability is basically common sense reduced to calculation; it makes us appreciate with exactitude what reasonable minds feel by a sort of instinct." So said Laplace. In the modern scientific and technological world it is even more important to understand probabilistic arguments. The key ideas of probability and random variables are discussed, including the binomial, Poisson, exponential and normal distributions.Objectives
On completion of this module, students should be able to: (a) state and use the basic rules of probability; (b) understand discrete probability modules such as the binomial, Poisson and geometric; (c) apply probability generating functions and expectation rules; (d) interpret and manipulate the distributions of continuous random variables such as the normal: (e) use a statistical package such as Minitab as an aid to understanding basic concepts.Syllabus
1. Introduction to probability, axioms, joint events and probability rules.
2. Conditional probability, Bayes¿ formula, independence.
3. Permutations and combinations.
4. Discrete random variables, mean and variance, linear properties of expectation.
5. Bernoulli trials, binomial distribution.
6. Poisson distribution. Geometric distribution.
7. Joint distribution of two discrete random variables, marginal distributions and independence.
8. Mean and variance of a linear function of two random variables. Covariance.
9. Probability generating functions.
10. Continuous random variables. Cumulative distribution function. Probability density function.
11. Mean and variance of a continuous random variable. Uniform distribution. Exponential distribution.
12. Functions of continuous random variables.
13. Normal distribution and use of tables. Normal approximation to the binomial.
Teaching methods
| Delivery type | Number | Length hours | Student hours |
| Lecture | 22 | 1.00 | 22.00 |
| Practical | 2 | 1.00 | 2.00 |
| Tutorial | 5 | 1.00 | 5.00 |
| Private study hours | 71.00 | ||
| Total Contact hours | 29.00 | ||
| Total hours (100hr per 10 credits) | 100.00 | ||
Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| In-course Assessment | . | 20.00 |
| Total percentage (Assessment Coursework) | 20.00 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Exams
| Exam type | Exam duration | % of formal assessment |
| Standard exam (closed essays, MCQs etc) | 2 hr 00 mins | 80.00 |
| Total percentage (Assessment Exams) | 80.00 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 31/03/2009
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- Undergraduate module catalogue
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