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- Probability & Statistics for Electrical Engineers
- Anology to digital logic
- basic probability and Venn diagrams
- Conditional probability
- Spy game, optional: detailed analysis of spy game
- Bayes Rule
- Monty Hall Matlab code
- Random variables
- Expectation
- Variance
- Binomial distribution
- Normal (Gaussian) distribution
- Some other distributions
- Joint discrete random variables
- Joint continuous random variables
- Covariance of random variables
- Linear combinations of random variables
- Chebyshev's theorem
- Introduction to statistics
- Central limit theorem, sampling distributions
- Examples using the different tables
- Confidence intervals
- Hypothesis testing
- Hypothesis testing continued
- Linear regression
- Inference on linear regression parameters
- Basic Concepts of Probability Theory
- Specifying Random Experiments
- The Axioms of Probability
- Computing Probabilities Using Counting Methods
- Conditional Probability
- Independence of Events
- Sequential Experiments
- Synthesizing Randomness: Random Number Generators
- Probabilities of Sequences of Events
- Discrete Random Variables
- The Notion of a Random Variable
- Discrete Random Variables and Probability Mass Function
- Expected Value and Moments of Discrete Random Variable
- Conditional Probability Mass Function
- Important Discrete Random Variables
- Generation of Discrete Random Variables
- One Random Variable
- The Cumulative Distribution Function
- The Probability Density Function
- The Expected Value of X
- Important Continuous Random Variables
- Functions of a Random Variable
- The Markov and Chebyshev Inequalities
- Transform Methods
- Basic Reliability Calculations
- Computer Methods for Generating Random Variables
- Entropy
- Pairs of Random Variables
- Two Random Variables
- Pairs of Discrete Random Variables
- The Joint cdf of X and Y
- The Joint pdf of Two Continuous Random Variables
- Independence of Two Random Variables
- Joint Moments and Expected Values of a Function of Two Random
- Variables
- Conditional Probability and Conditional Expectation
- Functions of Two Random Variables
- Pairs of Jointly Gaussian Random Variables
- Generating Independent Gaussian Random Variables
- Vector Random Variables
- Vector Random Variables
- Functions of Several Random Variables
- Expected Values of Vector Random Variables
- Jointly Gaussian Random Vectors
- Estimation of Random Variables
- Generating Correlated Vector Random Variables
- Sums of Random Variables and Long-Term Averages
- Sums of Random Variables
- The Sample Mean and the Laws of Large Numbers
- Weak Law of Large Numbers
- Strong Law of Large Numbers
- The Central Limit Theorem
- Central Limit Theorem
- Convergence of Sequences of Random Variables
- Long-Term Arrival Rates and Associated Averages
- Calculating Distribution’s Using the Discrete Fourier
- Transform
- Statistics
- Samples and Sampling Distributions
- Parameter Estimation
- Maximum Likelihood Estimation
- Confidence Intervals
- Hypothesis Testing
- Bayesian Decision Methods
- Testing the Fit of a Distribution to Data
- Random Processes
- Definition of a Random Process
- Specifying a Random Process
- Discrete-Time Processes: Sum Process, Binomial Counting Process,
- and Random Walk
- Poisson and Associated Random Processes
- Gaussian Random Processes, Wiener Process
- and Brownian Motion
- Stationary Random Processes
- Continuity, Derivatives, and Integrals of Random Processes
- Time Averages of Random Processes and Ergodic Theorems
- Fourier Series and Karhunen-Loeve Expansion
- Generating Random Processes
- Analysis and Processing of Random Signals
- Power Spectral Density
- Response of Linear Systems to Random Signals
- Bandlimited Random Processes
- Optimum Linear Systems
- The Kalman Filter
- Estimating the Power Spectral Density
- Numerical Techniques for Processing Random Signals
- Markov Chains
- Markov Processes
- Discrete-Time Markov Chains
- Classes of States, Recurrence Properties, and Limiting
- Probabilities 660
- Continuous-Time Markov Chains
- Time-Reversed Markov Chains
- Numerical Techniques for Markov Chains
- Queueing Theory
- The Elements of a Queueing System
- Little’s Formula
- The M/M/1 Queue
- Multi-Server Systems: M/M/c, M/M/c/c,
- Finite-Source Queueing Systems
- M/G/1 Queueing Systems
- M/G/1 Analysis Using Embedded Markov Chains
- Burke’s Theorem: Departures From M/M/c Systems
- Networks of Queues: Jackson’s Theorem
- Simulation and Data Analysis of Queueing Systems