This unit is composed of 4 initial general sections followed by two additional specializing sections. The 4 initial sections illustrate the basics of probability and statistics and are to be studied by all engineering disciplines. Following are two additional sections (5, 6) which are broken up either into (5s, 6s) focusing on useful statistical methods or (5p, 6p) which focus on probabilistic analysis of random signals. Sections (5s, 6s) will typically be studied by mechanical and civil engineering students while sections (5p, 6p) will typically be studied by electrical and mechatronics engineering students. Section 0 is intended only for tutorials and reviews basic maths used later on.

Literature:

·         [DeGr12]  M. H. DeGroot, M. J. Schervish, Probability and Statistics, 4th Edition, 2012. (Previous editions are also OK).

·         [LeGar08] A. Leon-Garcia, Probability, Statistics and Random Processes for Electrical Engineering, 3rd Edition 2008. (Previous editions are also OK).

·         There are dozens of additional similar suitable texts.

 Section Outline Lecture Notes in Brief Supplementary Reading Short Exercises and Tutorial Material Starred Exercises Comments and additional links 0 Mathematical review --tutorial only-- [DeGr12] 1.4 (pp 6-15) [DeGr12] 1.7, 1.8 (pp 25-41) [LeGar08] 2.1.3 (pp 25-30) [LeGar08] 2.3 (pp 41-47) Mathematical Software 1 Introduction: Sampling a proportion, proportions and probability, random variables, errors in sampling, simulation. [DeGr12] 1.1-1.3 (pp 1-6) [DeGr12] 1.5, 1.6 (pp 16-25) [DeGr12] 1.11 (pp 51-53) [DeGr12] 3.1-3.3 (pp 93-117) [DeGr12] 4.1 (pp 207-211) [DeGr12] 4.3 (pp 225-228) [DeGr12] 7.1 (pp 376-384) [DeGr12] 8.1 (pp 464-469) [DeGr12] 12.1 (pp 787-791) [LeGar08] 1.1-1.3 (pp 1-9) [LeGar08] 2.1 (pp 21-24) [LeGar08] 2.2 (pp 30-41) [LeGar08] 2.7 (pp 67-70) [LeGar08] 3.1-3.2 (pp 96-104) [LeGar08] 4.1-4.2-4.21 (pp 141-152) [LeGar08] 8.1-8.2 (pp 411-415) 2 Sampling distributions: Independence, Binomial, Hyper-Geometric and Gaussian (Normal) distributions as well as the central limit theorem. [DeGr12] 2.2 (pp 66 – 75) [DeGr12] 5.2-5.3 (pp 275 – 286) [DeGr12] 5.6 (pp 302-314) [DeGr12] 6.3 (pp 360-368) [DeGr12] 6.4 (pp 371-374) [LeGar08] 3.3 (pp 104-110) [LeGar08] 3.5.2 (pp 117-119) [LeGar08] 4.4.3 (pp 167-169) [LeGar08] 7.1.1 (pp 360-363) [LeGar08] 7.2 -7.3 (pp 365 - 377) A normal distribution table: NORMALTABLE.pdf 3 Point Estimation, Confidence intervals and statistical tests. [DeGr12] 8.5 (pp 485-494) [DeGr12] 9.1 (pp 530-547) [DeGr12] 9.2 (pp 550-557) [DeGr12] 9.9 (pp 617-620) [LeGar08] 8.4-8.5 (pp 430-455) [LeGar08] 8.7 (pp 462-468) test1_May9_2011.pdf (mechanical) 4 Jointly distributed random variables. Lecture_4_partB.pdf (mechatronics) [DeGr12] 3.4-3.5 (pp 118 – 141) [DeGr12] 3.7 (pp 152 – 159) [DeGr12] 4.6 (pp 248 – 255) [DeGr12] 5.9-5.10 (pp 333 – 344) [LeGar08] 5.1-5.6 (pp 233-261) [LeGar08] 5.9-5.10 (pp 278-286) [LeGar08] 6.1 (pp 303-309) [LeGar08] 6.3 (pp 318-322) [LeGar08] 6.4( pp 325-332) [LeGar08] 6.6 (pp 342-345) 5s Linear Statistical Models – Part A [DeGr12] 9.5-9.6 (pp 576-596) [DeGr12] Chapter 11 (pp 689-786) --no tutorial material for this section-- 6s Linear Statistical Models – Part B (mechanical) 5p Second order processes – Part A [LeGar08] 9.1-9.2 (pp 487-497) [LeGar08] 9.5 (pp 514-518) [LeGar08] 9.6 (pp 518-528) [LeGar08] 9.10 (pp 550-553) [LeGar08] Chapter 10 (pp 577-646) --no tutorial material for this section-- (mechatronics) Solution by Students 6p Second order processes – Part B