

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: Autocorrelation and covariance functions, power spectral density, response of linear timeinvariant 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.

