A Quick Tour of Probability and Statistics for
Final Year Engineering Students
(last updated by Yoni Nazarathy: May 24, 2011)

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)	Tutorial_0_23_05_11.pdf	Starred0_verApril10.pdf	Mathematical Software
1	Introduction: Sampling a proportion, proportions and probability, random variables, errors in sampling, simulation.	Lecture_1.pdf	[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)	Tutorial_1_22_05_11.pdf	Starred1_verApr13.pdf
2	Sampling distributions: Independence, Binomial, Hyper-Geometric and Gaussian (Normal) distributions as well as the central limit theorem.	Lecture_2.pdf	[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)	Tutorial_2_24_05_11.pdf	Starred2_verApril13.pdf	A normal distribution table: NORMALTABLE.pdf
3	Point Estimation, Confidence intervals and statistical tests.	Lecture_3.pdf	[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)	Tutorial_3_24_05_11.pdf	Starred3.pdf	Confidence Interval Demo test1_May9_2011.pdf (mechanical) test1Solution.pdf HWProject1.pdf (mechatronics) SolutionByStudents #1 SolutionByStudents #2
4	Jointly distributed random variables.	Lecture_4_partA.pdf 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)	Tutorial_4_24_05_11.pdf		Correlations Demo BivariateGaussianRandomVariables - Simple Nice Demo BivariateNormalDistribution Demo 2 BivariateNormalDistribution Demo 3
5s	Linear Statistical Models – Part A	Lecture_5s.pdf	[DeGr12] 9.5-9.6 (pp 576-596) [DeGr12] Chapter 11 (pp 689-786)	--no tutorial material for this section--		ANOVA Demo Percentiles of the F Distribution Table
6s	Linear Statistical Models – Part B	Lecture_6s.pdf				Least Squares Demo Confidence Interval for Regression Demo test2_May26_2011.pdf (mechanical) test2Solution.pdf
5p	Second order processes – Part A	Lecture_5p.pdf	[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--		PoissonProcess Demo RandomWalk Demo BrownianMotion Demo Simple Queue Demo Another Queue Demo HWProject2.pdf (mechatronics) Solution by Students
6p	Second order processes – Part B	Lecture_6p.pdf				FrequencySpectrum Demo StepAndImpulseResponse of (deterministic) LTI Demo Convolution Demo ConvolutionSum Demo DFT with Noise Demo