School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2019/20 Last Updated: 12 November 2019

MAT-20023 - Probability

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MAT-10046 Calculus and MAT-10047 Algebra.

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Probability is the mathematics of uncertainty and randomness. The module begins with classical notions of probability associated with the analysis of games of chance using cards, dice, etc. It then moves to the axiomatic treatment of the probability of random events. This leads to the definitions of statistical independence and conditional probability. The remainder of the module is concerned with a systematic study of discrete and continuous, univariate and bivariate, random variables, covering expectation, variance, covariance and the moment generating function.

The theory is applied to a wide range of theoretical and applied problems.

This module develops the following Keele Graduate attributes:

1. An open and questioning approach to ideas, demonstrating curiosity and independence of thought.

4. The ability to solve problems creatively using a range of different approaches and techniques, and to determine which techniques are appropriate for the issue at hand.

6. The ability to communicate clearly and effectively in written and verbal form.

The theory is applied to a wide range of theoretical and applied problems.

This module develops the following Keele Graduate attributes:

1. An open and questioning approach to ideas, demonstrating curiosity and independence of thought.

4. The ability to solve problems creatively using a range of different approaches and techniques, and to determine which techniques are appropriate for the issue at hand.

6. The ability to communicate clearly and effectively in written and verbal form.

The aims of the module are to study:

(a) an axiomatic treatment of probability, motivated by classical notions of chance;

(b) the theory of univariate and bivariate random variables and their distributions;

(c) applications of the theory of univariate and bivariate random variables and their distributions.

(a) an axiomatic treatment of probability, motivated by classical notions of chance;

(b) the theory of univariate and bivariate random variables and their distributions;

(c) applications of the theory of univariate and bivariate random variables and their distributions.

prove and apply results that are consequences of the axioms of probability: prove and apply results that are consequences of the axioms of probability: 1,2,

calculate and apply probability distributions, expectations and variances associated with univariate random variables: calculate and apply probability distributions, expectations and variances associated with univariate random variables: 1,2,

calculate and apply probability distributions, expectations, variances and covariances associated with bivariate random variables: calculate and apply probability distributions, expectations, variances and covariances associated with bivariate random variables: 1,2,

solve problems involving the concepts of independence and conditioning: solve problems involving the concepts of independence and conditioning: 1,2,

solve problems involving the concepts of independence and conditioning.:

calculate and apply probability distributions, expectations and variances associated with univariate random variables: calculate and apply probability distributions, expectations and variances associated with univariate random variables: 1,2,

calculate and apply probability distributions, expectations, variances and covariances associated with bivariate random variables: calculate and apply probability distributions, expectations, variances and covariances associated with bivariate random variables: 1,2,

solve problems involving the concepts of independence and conditioning: solve problems involving the concepts of independence and conditioning: 1,2,

solve problems involving the concepts of independence and conditioning.:

Lectures: 36 hours

Examples Classes: 12 hours

Continuous assessment preparation: 30 hours

Private study: 70 hours

Unseen examination: 2 hours

Examples Classes: 12 hours

Continuous assessment preparation: 30 hours

Private study: 70 hours

Unseen examination: 2 hours

None

Continuous assessment

Continuous assessment will consist of written coursework, problem sheets, class tests, or any combination thereof.

Two-hour end of module examination

The examination paper will consist of no less than five and not more than eight questions all of which are compulsory.