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ECE 313

PROBABILITY WITH ENGINEERING APPLICATIONS

MW SECTION - IYER

Course Outline (Tentative)

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I. Introduction

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- Motivation
- Course objectives/outline
- Probability theory, models and their uses, examples
- Definitions: sample space, elements, events
- Algebra of events (union, intersections, laws/axioms)
- Probability axioms and other useful relationships
- Basic procedure for problem solving and an example
- Combinatorial problems
- Introduction to measurements

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II. Conditional Probability and Independence of Events

- Definitions of conditional problems, multiplication rule
- Example
- Independent events and associated rules
- Application to reliability evaluation:
- Series systems
- Parallel redundancy
- Example: series-parallel system evaluation
- Theorem of total probability, Bayes' Formula

- Examples:
- Error-prone communication channel
- Non-series-parallel system

- Application to system reliability
- Preliminary performance /reliability measurements in-lab and on a campus system

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III. Bernoulli Trials

- TMR system with voter
- Multiple failure modes

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IV. Random Variables (Discrete)

- Introduction: random variables and associated event space
- Probability mass function
- Special discrete random variables and their distribution:
- Binomial
- Geometric
- Poisson
- Uniform

- Application to program/algorithmic analysis
- Performance measurements using SPEC and other benchmarks
- Preliminary project presentations

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V. Random Variables (Continuous)

- Mean, median, variance models
- Distribution function, probability density function
- Exponential distribution
- Application to reliability evaluation
- Other important distributions:
- Normal
- Hyper and hypo exponentials
- Weibull

- Expectations:
- Mean, median variance
- Expectation of function of random variables
- Mean time to failure
- Conditional expectation
- Inequalities and limit theorems
- Fault coverage and reliability

- Final project presentations

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VI. Summary and Overview