timed Random Signals and Noise assignment [Electrical Engineering ] -- 3

2. Introduction to Probability Theory Page in the pdf file [10 – 65] 2.1 Experiments, Sample Spaces, and Events 2.2 Axioms of Probability 2.3 Assigning Probabilities 2.4 Joint and Conditional Probabilities 2.5 Basic Combinatorics 2.6 Bayes’s Theorem 2.7 Independence 2.8 Discrete Random Variables 2.9 Engineering Application—An Optical Communication System [login to view URL] Variables, Distributions, and Density Functions Page in the pdf file [66 – 113] 3.1 The Cumulative Distribution Function 3.2 The Probability Density Function 3.3 The Gaussian Random Variable 3.4 Other Important Random Variables • 3.4.1 Uniform Random Variable • 3.4.2 Exponential Random Variable • 3.4.3 Laplace Random Variable • 3.4.4 Gamma Random Variable • 3.4.5 Erlang Random Variable • 3.4.6 Chi-Squared Random Variable • 3.4.7 Rayleigh Random Variable • 3.4.8 Rician Random Variable • 3.4.9 Cauchy Random Variable 3.5 Conditional Distribution and Density Functions 3.6 Engineering Application: Reliability and Failure Rates [login to view URL] on a Single Random Variable Page in the pdf file [114 – 178] 4.1 Expected Value of a Random Variable 4.2 Expected Values of Functions of Random Variables 4.3 Moments 4.4 Central Moments 4.5 Conditional Expected Values 4.6 Transformations of Random Variables • 4.6.1 Monotonically Increasing Functions • 4.6.2 Monotonically Decreasing Functions • 4.6.3 Nonmonotonic Functions 4.7. Characteristic Functions 4.8. Probability-Generating Functions 4.9 Moment-Generating Functions 4.10 Evaluating Tail Probabilities 4.11 Engineering Application—Scalar Quantization 4.12 Engineering Application—Entropy and Source Coding [login to view URL] of Random Variables Page in the pdf file [179 – 244] 5.1 Joint Cumulative Distribution Functions 5.2 Joint Probability Density Functions 5.3 Joint Probability Mass Functions 5.4 Conditional Distribution, Density, and Mass Functions 5.5 Expected Values Involving Pairs of Random Variables 5.6 Independent Random Variables 5.7 Jointly Gaussian Random Variables 5.8 Joint Characteristic and Related Functions 5.9 Transformations of Pairs of Random Variables 5.10 Complex Random Variables 5.11 Engineering Application: Mutual Information, Channel Capacity, and Channel Coding [login to view URL] Random Variables Page in the pdf file [245 – 288] 6.1 Joint and Conditional PMFs, CDFs, and PDFs 6.2 Expectations Involving Multiple Random Variables 6.3 Gaussian Random Variables in Multiple Dimensions 6.4 Transformations Involving Multiple Random Variables • 6.4.1 Linear Transformations • 6.4.2 Quadratic Transformations of Gaussian Random Vectors • 6.4.3 Order Statistics • 6.4.4 Coordinate Systems in Three Dimensions 6.5 Estimation and Detection • 6.5.1 Maximum a Posteriori Estimation • 6.5.2 Maximum Likelihood Estimation • 6.5.3 Minimum Mean Square Error Estimation 6.6 Engineering Application: Linear Prediction of Speech [login to view URL] Sums and Sequences Page in the pdf file [289 – 333] 7.1 Independent and Identically Distributed Random Variables • 7.1.1 Estimating the Mean of IID Random Variables • 7.1.2 Estimating the Variance of IID Random Variables • 7.1.3 Estimating the CDF of IID Random Variables 7.2 Convergence Modes of Random Sequences • 7.2.1 Convergence Everywhere • 7.2.2 Convergence Almost Everywhere • 7.2.3 Convergence in Probability • 7.2.4 Convergence in the Mean Square Sense • 7.2.5 Convergence in Distribution 7.3 The Law of Large Numbers 7.4 The Central Limit Theorem 7.5 Confidence Intervals 7.6 Random Sums of Random Variables 7.7 Engineering Application: A Radar System