Chapter 2:
Brief Review of Probabilistic Modeling
 CONTENTS Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8
 2 Brief Review of Probabilistic Modeling 2.1 Experiment, Sample Space, and Events 2.2 Event Probabilities 2.3 Random Variables 2.4 Probability Mass Function 2.5 Conditional PMF's and Independence 2.6 Functions of Random Variables 2.7 Expectation 2.8 The z-transform 2.9 Often-Used PMF's 2.9.1 Bernoulli PMF 2.9.2 Geometric PMF 2.9.3 Binomial PMF 2.9.4 Poisson PMF 2.10 Probability Density Functions 2.10.1 Conditional PDF's and independence 2.10.2 Expectation 2.10.3 Unit impulse function 2.10.4 The s-transform 2.11 Often-Used PDF's 2.11.1 Uniform PDF 2.11.2 Exponential PDF 2.11.3 Erlang PDF 2.11.4 Gaussian PDF 2.12 Poisson Process 2.12.1 Postulates of a Poisson process 2.12.2 Interarrival times 2.12.3 Unordered arrival times 2.12.4 Multiple independent Poisson processes 2.13 Random Incidence 2.14 Pedestrian Crossing Problem 2.15 Conclusion *** Problems