Description:  Introduction to probability and statistics, including applications relevant to electrical and computer engineering.  Includes extensive coverage of random variables, introduces random processes, and illustrates their importance in communications, signal processing, and networking.

Preprequisites:  MTH 249 or MTH 251 and MTH 222 or MTH 231

Objectives:

• Solve simple probability problems that arise in electrical and computer engineering applications.
• Use random processes to model phenomena that arise in real-world applications with particular emphasis on communications systems and/or networks.
• Determine key properties (e.g., autocorrelation, spectral density) of the output of a linear system when the system and input random process are known.
• Use Matlab to generate random data with a specified ditribution.

Tentative Topics:

• Set operations and probabilistic models.
• Probability axioms, joint and conditional probability, Bayes' Rule and total probability; independence; counting.
• Discrete random variables, probability mass function, and moments.
• Continuous random variables, Gaussian and other probability density functions.
• Jointly distributed random variables, conditional probability and expectiation; independent random variables; covariance and correlation; derived distributions.
• Sums and transformations of random variables; sample mean and law of large numbers; central limit theorem.
• Random processes and correlation functions.
• Stationarity and spectral density; review of linear system fundamentals.
• Random signals and linear systems.
• Communication system evaluation with random noise; spectral characteristics of system response.
• Noise bandwidth and noise modeling; matched filters.
• Poisson process; modeling traffic in communication networks; Markov chains; performance analysis of communication networks.