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