| CODE | SOR2210 | ||||||||
| TITLE | Families of Random Variables and Random Vectors | ||||||||
| UM LEVEL | 02 - Years 2, 3 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | Not Applicable | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||
| DESCRIPTION | Functions of Random Variables - Transformations of Random Variables - Moment Generating Functions - Joint Distributions - Independent Random Variables - Sequences of Identically Distributed Random Variables - Sums of Random Variables Sampling Distributions - The Sampling Problem - Sample Mean - Sample Variance - Central Limit Theorem - The x2-Distribution - The t-distribution - The F-distribution Bivariate Random Variables - Bivariate density functions and distributions - The Bivariate normal distribution - Conditional density, expectation and variance with reference to bivariate distributions - Covariance and Correlation Random Vectors - Multivariate Density and Distribution Functions - Marginal and Conditional Distributions - Expectation of Random Vector - Covariance Matrix, Correlation Matrix - Partial Correlation - Data Matrices and Transforming them Linearly - Sample Mean, Sample Covariance, Sample Correlation - P-variate Normal Distribution - Matrix Transformations of Normal Random Vector - Distribution of Quadratic Forms Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: - Formulate theoretical models of system of processes or realities, and of ones knowledge about them within the world around us, involving uncertainty in some essential way; - Comprehend how a finite number of observations coming from the particular system under study can be used to modify, refine and organize our knowledge of the system with reference to the postulated model; - Recall and apply major theoretical results (such as the Central Limit Theorem), which form the foundations of various topics, which the students cover in their second and third year; - Explain the important concepts of joint and conditional distributions; - Discuss how theoretical results on univariate random variables can be extended to multivariate random vectors by applying results from matric algebra and probability theory. 2. Skills By the end of the study-unit the student will be able to: - Explain how the distribution of a random variable X changes after it is transformed using some function g; - Derive moments of the distribution of random variables and their transformations; - Derive the joint and conditional distributions for a sequence of random variables, and the respective expectations and variances; - Derive the sampling distribution of a number of statistics (e.g. mean, variance, quantiles). Suggested texts: - Freund, John E. ( 1992 ) Mathematical Statistics, Prentice Hall - Hogg, R.V. and Craig, A.T. ( 1978 ) Introduction to Mathematical Statistics, Macmillan - Van der Waerden, B.L. ( 1969 ) Mathematical Statistics, Springer Verlag - Mardia, K.V., Kent, J.T. and Bibby J.M. ( 1995 ) Multivariate Analysis, Academic - Searle,S.R. ( 1971 ) Linear Models, J.Wiley & Sons, New York - Seber, G.A.F.( 1977 ) Linear Regression Analysis, J.Wiley & Sons, New York - Knight K., ( 1999 ) Mathematical Statistics, CRC - Roussas George G., ( 1997 ) A Course in Mathematical Statistics, Academic Press |
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| ADDITIONAL NOTES | Pre-requisite Study-units: SOR1110, SOR1220 | ||||||||
| STUDY-UNIT TYPE | Lecture | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Liberato Camilleri Fiona Sammut |
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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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