|
|
Contents
|
|
| Week 1: |
Basic principle of counting, permutation, combination |
| Week 2: |
Axioms of probability, conditional probability |
| Week 3: |
Independence, chain rule, Bayes rule, random variables |
| Week 4: |
Discrete random variables: Probability mass and cummulative distribution functions, expected value and variance |
| Week 5: |
Bernoulli, binom, Poisson and geometric random variables |
| Week 6: |
Continuous random variables: Probability density and cummulative distribution functions, expected value and variance |
| Week 7: |
Uniform, normal and exponential random variables |
| Week 8: |
Midterm exam |
| Week 9: |
A function of random variables, jointly distributed random variables |
| Week 10: |
Marginal and conditional densities, correlation and covariance |
| Week 11: |
Sum of independent random variables, linear mean square error estimation |
| Week 12: |
Conditional expectation, moment generating functions |
| Week 13: |
Limit theorems: Markov and Chebyshev inequilities, weak law of large numbers, central limit theorem |
| Week 14: |
Random processes: Auto-correlation and covariance functions, power spectral density, response of linear time-invariant systems to random processes |
| Week 15*: |
- |
| Week 16*: |
Final Exam |
| Textbooks and materials: |
[1] Probability of Statistics for Engineering & Scientists. Walpole E.W., Myers R.H., Myers S.L., Ye K. Pearson Education, Prentice Hall Inc.
[2] Probability and Random Processes with Applications to Signal Processing and Communications, Scott L. Miller, Donald G. Childers |
| Recommended readings: |
[1] A First Course in Probability, S. Ross, Prentice Hall
[2] Probability Random Variables and Stochastic Processes, A.Papolis, McGraw Hill |
|
|
* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
|
|
