| CODE | SOR1110 | ||||||||
| TITLE | Probability | ||||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 5 | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||
| DESCRIPTION | - Historical background; - Combinatorial and Geometric Probability; - Probability Spaces; - Conditional Probability; - Random Variables. Discrete Distributions: - Uniform, Binomial, Poisson, Geometric, Multinomial and Hypergeometric Distributions. Continuous Distributions: - Uniform, Exponential, Gamma, Beta and Normal Distributions; - Expectations and Variances; - Chebychev Inequality, Law of Large Numbers, Approximations to Binomial Distribution, Convergence in a Probabilistic Setting. Study-Unit Aims: The main aim of this study-unit is that of familiarizing the students with the theoretical and practical framework underlying Probability, Probability spaces, the concept of a random variable, probability density functions, and cumulative distribution functions in both the discrete and continuous setting. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Be able to understand how to compute probability in the case where the set of all possible outcomes is finite and also in the case where the set of all outcomes is uncountably infinite; - Be familiar with the concept of Probability Space; - Have developed a sound background in the theory of conditional probability; - Have a better appreciation of the Bayes’ rule and the law of total probability; - Be able to identify the type of distribution to be used in a variety of different scenarios; - Have the theoretical foundations required to be able to find the expectation and variance of a random variable; - Have the theoretical foundations required to apply the law of large numbers and the Poisson and normal approximation to the binomial distribution. 2. Skills: By the end of the study-unit the student will be able to: - Use the theoretical knowledge gained in the study unit to compute the probability of scenarios where the set of possible is outcomes is either finite or infinite; - Know which probability distribution to use in different scenarios; - Know how to compute the expectation and variance of a number of probability distributions; - Use various statistical packages to obtain estimates of the expectation and variance; - Use the material learnt to understand the theoretical and practical importance of the Poisson and Normal approximation to the binomial distribution. Main Text/s and any supplementary readings: Suggested texts: - Chung, K. L. (1979) Elementary Probability Theory with Stochastic Processes, Springer - Ross, S. (1997) Introduction to Probability Models, Academic - Freund, J. E. and Walpole R.E. (1987) Mathematical Statistics, Prentice Hall Inc. - Feller, W. (1971) An Introduction to Probability Theory and its Applications, Wiley - Grimmett, G.R. and Stirzaker, D.R. (1994) Probability and Random Processes, Clarendon Press, Oxford - Renyi, A. (1970) Probability Theory, North Holland - Shiryaev, A.N. (1996) Probability, Springer |
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| ADDITIONAL NOTES | Pre-requisite Qualification: Advanced Level Pure Mathematics | ||||||||
| STUDY-UNIT TYPE | Lecture | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Derya Karagoz |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years. |
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