Fundamentals of Probability and Statistics for Engineers

viiiContents3.2.3 Probability Density Function for Continuous RandomVariables 443.2.4 Mixed-Type Distribution 463.3 Two or More Random Variables 493.3.1 Joint Probability Distribution Function 493.3.2 Joint Probability Mass Function 513.3.3 Joint Probability Density Function 553.4 Conditional Distribution and Independence 61Further Reading and Comments 66Problems 674 EXPECTATIONS AND MOMENTS 754.1 Moments of a Single Random Variable 764.1.1 Mean, Median, and Mode 764.1.2 Central Moments, Variance, and Standard Deviation 794.1.3 Conditional Expectation 834.2 Chebyshev Inequality 864.3 Moments of Two or More Random Variables 874.3.1 Covariance and Correlation Coefficient 884.3.2 Schwarz Inequality 924.3.3 The Case of Three or More Random Variables 924.4 Moments of Sums of Random Variables 934.5 Characteristic Functions 984.5.1 Generation of Moments 994.5.2 Inversion Formulae 1014.5.3 Joint Characteristic Functions 108Further Reading and Comments 112Problems 1125 FUNCTIONS OF RANDOM VARIABLES 1195.1 Functions of One Random Variable 1195.1.1 Probability Distribution 1205.1.2 Moments 1345.2 Functions of Two or More Random Variables 1375.2.1 Sums of Random Variables 1455.3 m Functions of n Random Variables 147Reference 153Problems 1546 SOME IMPORTANT DISCRETE DISTRIBUTIONS 1616.1 Bernoulli Trials 1616.1.1 Binomial Distribution 162TLFeBOOK