·
[LeGar08] A.
LeonGarcia, Probability, Statistics and Random Processes for Electrical
Engineering, 3rd Edition 2008. (Previous editions can also be used).
·
[Gub06] J.
A. Gubner, Probability and Random Processes for
Electrical and Computer Engineer, 2006.
·
[Ro10]
S.
M. Ross, Introduction to Probability Models, 10th Edition, 2010. (Previous
editions are also OK).
·
[Kul99] V.
G. Kulkarni, Modelling, Analysis, Design, and Control
of Stochastic Systems, 1999.
·
[HoPoSt72] P.
G. Hoel, S. C. Port, C. J. Stone, Introduction to
Stochastic Processes, 1972.
·
[Pap91] A.
Papoulis, Probability, Random Variables and Stochastic Processes, 3rd Edtion, 1991. (Previous editions are also OK).
·
[Dur99] R. Durret,
Essentials of Stochastic Processes, 1999.
·
[DeGr12]
M.
H. DeGroot, M. J. Schervish,
Probability and Statistics, 4th Edition, 2012. (Previous editions are also
OK).
Section 
Outline 
[LeGar08] 
Home Assignments 
Comments 
0a 
Mathematical background: Sets, Counting, Series and
Summations. 
 
 
Math
background notes (partially complete) Demo:
ComparingBasicNumericalIntegrationMethods Wiki:
Inclusion Exclusion Principle Wiki:
List of trigonometric identities 
0b 
Mathematical background: Basic integration review,
Complex Numbers, Fourier Transforms. 
 

0c 
Mathematical background: Convolutions, linear time
invariant systems, frequency response. 
 

1a 
Introduction: Stochastic Modelling – an uncertain world – scalar
uncertain results. 
1.1 
 
Demo:
ScalingsOfAGIG1QueueRealization 
1b 
Introduction: Stochastic Modelling – an uncertain world – random
signals, random packets and other models. 
1.4 

2a 
Probability spaces: Generating Uniforms (simulation),
Events, probability function, basic axioms. 
2.7 

Demo:
MersenneTwisterAndFriends Demo:
ApproximatingPiByTheMonteCarloMethod 
2b 
Probability spaces: Independence, conditional
probability, law of total probability, Bayes’
rule. 
2.4 

3a 
Random Variables: Discrete random variables,
PMFs, CDFs, expectations: mean, moments, variance, Generation (simulation). 
3.1 

3b 
Random Variables: Continuous random variables,
PDFs (density), expectations: mean, moments, variance, Markov
inequality. 
4.1 

3c 
Random Variables: functions of random
variables, inverse probability transform, Random number generation, solving
basic problems by basic simulation. 
4.5 

4a 
Useful (families) of
discrete distributions: Discrete
uniform, binomial, geometric, hypergeometric, negative binomial, Poisson. 
3.5 
Demo:
BinomialProbabilityDistribution Demo: GeometricDistribution Demo:
TheHypergeometricDistribution 

4b 
Useful (families) of
continuous distributions: Uniform, exponential, normal (Gaussian), gamma, beta,
Cauchy. 
4.4 
Demo:
TheContinuousUniformDistribution Demo: TheExponentialDistribution 

Test
on Sections 14 

5a 
Joint distributions: Joint distribution of
pairs (discrete and continuous). Random vectors. Independence. Joint moments.
Joint Gaussian. 
5.1 
Demo:
DiscreteMarginalDistributions Demo:
JointDensityOfBivariateGaussianRandomVariables 

5b 
Joint distributions: Conditional distributions,
expectation and variance. Conditional distribution of Gaussians. Mean vector
and covariance matrix. Jointly Gaussian random vectors. 
5.7 

5c 
Joint distributions: Transformations and
generation. 
5.8 

6a 
Estimation: MAP and ML Estimators,
Minimum MSE Linear Estimators and Minimum MSE Estimators. 
6.5 

6b 
Estimation: Estimation using a vector
observations, examples, parameter estimation, ML parameter estimation,
CramerRao (in brief). 
6.5 


7a 
Transforms, Sums and long
term averages: Transforms
of random variables, distribution of i.i.d sums, 
4.7 

7b 
Transforms, Sums and long
term averages: Law
of large numbers, central limit theorem, renewal counting processes. 
7.2 

8a 
Random process basics: Definitions, distribution,
mean function, covariance function, multiple processes, simple examples
(Binomial process etc..). 
9.1 

8b 
Random processes basics: 
9.4 

9a 
Signal Level Processes: Stationary processes (and
wide sense stationary), cyclostationary processes,
time averages and ergodic theorems (nonrigorous). 
9.6 
HW Project #5 

9b 
Signal Level Processes: Fourier series and KarhunenLoeve expansions. 
9.9 

10a 
Signal Processing Basics: Power spectral density,
response of linear systems to signals, sampling and modulation (in brief). 
10.1 

10b 
Signal Processing Basics: 
10.4 

11a Cancelled 
Packet Level Processes: Idea of Markov processes,
discrete time Markov chains, steady state, brief description of classes and
recurrence properties. 
11.1 
HW Project #6 cancelled 
Demo:
TransitionMatricesOfMarkovChains 
11b Cancelled 
Packet Level Processes: Continuous time Markov
chains, birthdeath chains with queueing examples,
numerical techniques (steady state solutions and simulation). 
11.4 

12a Cancelled 
Queuing Theory: Terminology, Little’s
formula, M/M/1 FCFS waiting time distribution. 
12.1 

12b cancelled 
Queuing Theory: M/G/1 queue (in brief), Jackson Networks (in brief),
simulation and data analysis of queuing systems. 
12.6 
