CS 278 Probability Models & Statistics 121 (4). Advanced probability, discrete time Markov chains, Poisson processes, continuous time Markov chains. Queuing or simulation as time permits. Prerequisite: Statistics 120A.
| Lectures |
Topic |
Material |
Sections from Ross |
| 1-2 |
Introduction |
course outline, policies |
|
| Review of probability |
sample space, events, probability, conditional probability, independence, Bayes, total probability |
1.1-1.6 |
| Random variables, PMF, PDF, expectation, variance, joint events, joint RVs |
2.1-2.5 |
| 3-6 |
Advanced probability |
indep RVs, correlation, conditional density, conditional expectation, functions of a R.V., cases |
2.4-2.5, 3.1-3.5 |
| sequences of RVs, convergence in distribution |
2.7-2.8 |
| Law of large numbers, central limit theorem |
2.7-2.8 |
| 7-9 |
Discrete time Markov chains |
transition matrices, communication |
4.1-4.3 |
| passage times, recurrence |
4.3 |
| steady state distribution, time reversibility |
4.4, 4.8 |
| 10-12 |
Poisson processes |
interarrival time characterization |
5.1-5.3 |
| number of events characterizations |
5.3 |
| multiplexing, demultiplexing |
5.3 |
| 11/17/09 |
Midterm |
|
|
| 13-14 |
Continuous time Markov chains |
characterizations, stationary distribution |
6.1-6.2, 6.4-6.5 |
| rewards, birth & death chains, time reversibility |
6.3, 6.6 |
| 15-17 |
Queuing |
M/M/1 queue model, performance |
8.1-8.3 |
| finite queues, multiple serves, infinite servers |
8.3, 8.9 |
| networks of queues |
8.4 |
| 12/1/09, 12/3/09, 12/10/09 |
Project presentations |
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