A

B

C

D

-

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* the sum of a  geometric series  and  power series for exp(x)

* basic calculus: the chain rule for differentiation and use of logarithms

SAQs - Solution Available Questions

Problems at the end of each chapter

Examples within each chapter

Week of August 25

0

HW 0 will not be graded

7:00:00pm for all HW deadlines below

* how to specify a set of outcomes, events, and probabilities for a given experiment (Ch 1.2)

* set theory (e.g. de Morgan's law) (Ch 1.2)

[Umrawal Lecture 1], [Umrawal Lecture 2], [Umrawal Lecture 3]

SAQs, (on p. 20) for Sections 1.2

Problems (p. 21-22) 1.2, 1.4, 1.6b, 1.8

Week of September 1

1

9/12

* using principles of counting and over counting; binomial coefficients (Ch 1.3-1.4) [ILLINI,  SAQ 1.3, SAQ 1.4, PokerIntro, PokerFH2P]

* random variables, probability mass functions, and mean of a function of a random variable (LOTUS) (Ch 2.1, first two pages of Ch 2.2) [pmfmean]

* scaling of expectation, variance, and standard deviation (Ch 2.2) [SAQ 2.2]

[Umrawal Lecture 4], [Umrawal Lecture 5]

SAQs (p. 20, 74) for Sections 1.3-1.4, 2.2

Problems (p. 23-24, 77-80) 1.10, 1.12, 2.2, 2.4, 2.6, 2.8, 2.10

Optional: [SAQ 1.5]

Week of September 8

2

9/19

* conditional probability (Ch 2.3) [team selection] [SAQ 2.3]

*law of total probability (Ch 2.10) [deuce] [SAQ 2.10]

*Bayes formula (Ch. 2.10)

* independence of events and random variables (Ch 2.4.1-2.4.2) [SimdocIntro] [Simdoc-Minhash1]

SAQs (p. 74-76) for Sections 2.3, 2.10

Problems (p. 81-82, 86-87) , 2.12, 2.14, 2.16, 2.32, 2.34

Week of September 15

3

9/26

* binomial distribution (how it arises, mean, variance, mode) (Ch 2.4.3-2.4.4) [SAQ 2.4] [bestofseven]

* geometric distribution (how it arises, mean, variance, memoryless property) (Ch. 2.5) [SAQ 2.5]

* Bernoulli process (definition, connection to binomial and geometric distributions) (Ch 2.6) [SAQ 2.6]

* Poisson distribution (how it arises, mean, variance) (Ch 2.7) [SAQ 2.7]

SAQs (p. 74-75) for Section 2.4-2.7

Problems (p. 82-84) 2.18, 2.20, 2.22, 2.24

Week of September 22

4

10/3

* maximum likelihood parameter estimation (definition, how to calculate for continuous and discrete parameters) (Ch 2.8) [SAQ 2.8]

* Markov and Chebychev inequalities (Ch 2.9)

* confidence intervals (definitions, meaning of confidence level) (Ch 2.9) [SAQ 2.9,Simdoc-Minhash2]

* hypothesis testing -- probability of false alarm and probability of miss (Ch. 2.11)

* ML decision rule and likelihood ratio tests (Ch 2.11) [SAQ 2.11]

SAQs (p. 75-76) for Sections 2.8, 2.9, 2.11

Problems (p. 85-86, 88-90) 2.26, 2.28, 2.30, 2.36a-b, 2.38, 2.40a

Week of September 29

5

10/10

* MAP decision rules (Ch 2.11)

* union bound and its application (Ch 2.12.1) [SAQ 2.12]

* cumulative distribution functions (Ch 3.1) [SAQ 3.1]

* probability density functions (Ch 3.2) [SAQ 3.2] [simplepdf]

SAQs (p. 76, 146) for Sections 2.11, 2.12, 3.1-3.2

Problems (p. 88-92, 149-151) 2.36, 2.40, 2.42, 2.44, 2.46, 3.2, 3.4, 3.6, 3.8

Week of October 6

6

10/17

* uniform distribution (Ch 3.3) [SAQ 3.3]

* exponential distribution (Ch 3.4) [SAQ 3.4]

* Poisson processes (Ch 3.5) [SAQ 3.5]

* Erlang distribution (Ch 3.5.3)

SAQs (p 147) for Sections 3.3-3.5

Problems (p. 151-152) 3.10, 3.12, 3.14

Week of October 13

7

10/24

* scaling rule for pdfs (Ch. 3.6.1)

* Gaussian (normal) distribution (e.g. using Q and Phi functions) (Ch. 3.6.2) [SAQ 3.6] [matlab help including Qfunction.m]

* the central limit theorem and Gaussian approximation (Ch. 3.6.3) [SAQ 3.6]

SAQs (p. 147) for Sections  3.6

Problems (p. 152-154) 3.16, 3.18, 3.20

Week of October 20

8

10/31

* ML parameter estimation for continuous type random variables (Ch. 3.7) [SAQ 3.7]

* the distribution of a function of a random variable (Ch 3.8.1) [SAQ 3.8]

* generating random variables with a specified distribution (Ch 3.8.2)

SAQs (pp. 147) for Sections 3.7, 3.8

Problems (pp. 154-159) , 3.22, 3.24, 3.26, 3.28, 3.30, 3.32, 3.34a, 3.38a-b,d

Week of October 27

9

11/7

* binary hypothesis testing for continuous type random variables (Ch 3.10) [SAQ 3.10]

* joint CDFs (Ch 4.1) [SAQ 4.1]

* joint pmfs (Ch 4.2) [SAQ 4.2]

SAQs (p. 148, 223) for Sections 3.10, 4.1-4.2

Problems (p. 226) 4.2

Week of November 3

10

11/14

* joint pdfs (Ch 4.3) [SAQ 4.3]

* joint pdfs of independent random variables (Ch 4.4) [SAQ 4.4]

* distribution of sums of random variables (Ch 4.5) [SAQ 4.5]

SAQs (p. 223-224) for Sections 4.3-4.5

Problems (p. 226-229) 4.4, 4.6, 4.8, 4.10, 4.12, 4.14

Week of November 10

11

11/21

* more problems involving joint densities (Ch 4.6) [SAQ 4.6]

* joint pdfs of functions of random variables (Ch 4.7) [SAQ 4.7] (Section 4.7.2 and 4.7.3 will not be tested in the exams)

* correlation and covariance: scaling properties and covariances of sums (Ch 4.8) [SAQ 4.8]

SAQs (p. 224) for Sections 4.6-4.8

Problems (p. 229-231) 4.16, 4.18, 4.20, 4.22

Week of November 17

12

12/5

* sample mean and variance of a data set, unbiased estimators (Ch 4.8, Example 4.8.7)

* minimum mean square error unconstrained estimators (Ch 4.9.2)

* minimum mean square error linear estimator (Ch 4.9.3) [SAQ 4.9]

SAQs (p.225) for Sections 4.9

Problems (p. 231-233) 4.24, 4.26, 4.28

Week of December 1

13

12/10

* law of large numbers (Ch 4.10.1)

* central limit theorem (Ch 4.10.2) [SAQ 4.10]

* joint Gaussian distribution (Ch 4.11) (e.g. five dimensional characterizations) [SAQ 4.11]

SAQs (p.225) for Sections 4.10-4.11

Problems (p. 233-237) 4.30, 4.32, 4.34, 4.36, 4.38, 4.40, 4.42

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