Table of Contents

Preface; 1 PROBABILITY; 1.1 Brief History of Probability; 1.2 Sample Space and Events; 1.3 Classical and Empirical Probability; 1.4 Axiomatic Definition of Probability; 1.5 Conditional Probability; 1.6 Total Probability; 1.7 Bayes' Theorem; 2 RANDOM VARIABLE; 2.1 Definition of a Random Variable; 2.2 Distribution Function of a Random Variable; 2.3 Discrete Random Variable; 2.4 Continuous Random Variable; 2.5 Mathematical Expectation; 2.6 Chebyshev's Inequality; 2.7 Moments of a Random Variable; 2.8 Moment Generating Function; 2.9 Characteristic Function; 3 STANDARD PROBABILITY DISTRIBUTIONS. 3.1 Degenerate Distribution; 3.2 Bernoulli Distribution; 3.3 Binomial Distribution; 3.4 Poisson Distribution; 3.5 Geometric Distribution; 3.6 Negative Binomial Distribution; 3.7 Uniform Distribution; 3.8 Exponential Distribution; 3.9 Gamma Distribution; 3.10 Weibull Distribution; 3.11 Normal Distribution; 3.12 Functions of a Random Variable; 4 TWO-DIMENSIONAL RANDOM VARIABLES; 4.1 Joint Distribution Functions; 4.2 Marginal Distributions; 4.3 Conditional Distributions; 4.4 Expectation; 4.5 Sums of Independent Random Variables; 4.6 Functions of Random Variables; 4.7 Covariance; 4.8 Conditional Expectation; 4.9 Correlation and Regression; 4.10 Central Limit Theorem; 5 RANDOM PROCESSES; 5.1 Definition and Description of Random Processes; 5.2 Stationary Random Processes; 5.3 Autocorrelation and Cross-correlation Functions; 5.4 Ergodic Process; 5.5 Markov Process; 5.6 Binomial, Poisson and Normal Processes; 5.7 Sine Wave Process; 5.8 Birth and Death Process; 6 SPECTRAL ANALYSIS OF RANDOM PROCESSES; 6.1 Autocorrelation and Cross-correlation Functions; 6.2 Power Spectral Density and Cross-spectral Density Functions; 6.3 Linear Systems with Random Inputs; 7 QUEUING THEORY; 7.1 Basics of Queuing Models; 7.2 Model I (M=M=1): (/FIFO) Model, Single Server with Infinite Capacity; 7.3 Model II (M=M=s): (/FIFO) Model, Multiple Server with Infinite Capacity; 7.4 Model III (M=M=1): (k/FIFO) Model, Single Server with Finite Capacity; 7.5 Model IV (M=M=s): (k/FIFO) Model, Multiple Server with Finite Capacity; 7.6 The (M=G=1) Queuing System; Answers to Problems; Bibliography; Index.

About the Author

V. Sundarapandian, DSc, is Professor and Academic Convenor, Indian Institute of Information Technology and Management (IIITM-K), Thiruvananthapuram, Kerala. He has more than 15 years of experience in teaching and research. Professor Sundarapandian is a life member of System Society of India and ISTE and has won numerous awards and honours for his contributions in nonlinear control systems. He has published many research papers in reputed international journals and has authored the book Numerical Linear Algebra (published by PHI Learning).