Probability, Stochastic Processes and Statistics: Course Syllabus and Tutorial Questions, Assignments of Probability and Statistics

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19I401 -

PROBABILITY, STOCHASTIC PROCESSES AND STATISTI

CS

19I401 - PROBABILITY, STOCHASTIC PROCESSES AND STATISTICS

Chapter 1: PROBABILITY AND DISCRETE RANDOM VARIABLES

Chapter 2: CONTINUOUS RANDOM VARIABLES

Chapter 3: PAIRS OF RANDOM VARIABLES

Chapter 4: STOCHASTIC PROCESSES

Chapter 5: STATISTICAL INFERENCE

Week -

• (^) Families of discrete random variables o (^) Binomial o (^) Poisson o (^) Geometric random variables

Text Books: T1. Roy D Yates and David J Goodman, “Probability and Stochastic Processes - A friendly Introduction for Electrical and Computer Engineers”, Wiley India, New Delhi, 2014. T2. Ronald E. Walpole, Raymond H Myers, Sharon L Myers and Keying Ye, “Probability and Statistics for Engineers and Scientists”, Pearsons, New Delhi, 2016

Families of Discrete Random Variables

1. Bernoulli trials

2. Binomial distribution

3. Geometric

4. Hypergeometric distribution

5. Poisson distribution etc…

Families of Discrete Random Variables

Binomial Random Variables

Geometric Random Variables

Poisson Random Variables

Introduction: The probability model of a Poisson random variable describes phenomena that occur randomly in time. While the time of each occurrence is completely random, there is a known average number of occurrences per unit time. The Poisson model is used widely in many fields. For example, the arrival of information requests at a World Wide Web server, the initiation of telephone calls, and the emission of particles from a radioactive source are often modeled as Poisson random variables. We will return to Poisson random variables many times in this text. At this point, we consider only the basic properties.