14:332:226 Probability and Random Processes

Course catalog description: Probability and its axioms, conditional probability, independence, counting, random variables and distributions, functions of random variables, expectations, order statistics, central limit theorem, confidence intervals, hypothesis testing, estimation of random variables. Random processes and their characterization, autocorrelation function.

Credits and contact hours: 3 credits; 1 hour and 20-minute session twice a week, every week

Pre-Requisite courses: 01:640:251 or 01:640:291

Co-Requisite courses: None

Topics Covered:

  • Experiments, models, probability axioms, conditional probability, independent events
  • Sequential experiments, tree diagrams, counting methods, independent trials 
  • Discrete random variables; probability mass function (PMF), cumulative distribution function (CDF)
  • Expected values,functions of one discrete random variable, variance and standard deviation, conditional PMF
  • Continuous random variables, probability density function (PDF), expectation
  • Gaussian random variables, delta functions and mixed random variables, functions of continuous random variables, derived distributions, conditional PDF 
  • Pairs of random variables; joint and marginal PMF, joint CDF, joint and marginal PDF
  • Functions of a pair of random variables, expected values, covariance and correlation, conditioning by an event
  • Conditioning by a random variable, independent random variables, bivariate Gaussian random variables
  • Multiple random variables; marginal distributions, independent and identically distributed (IID) random sequences, weak law of large numbers
  • Distributions of sums of random variables; convolution, moment generating function, central limit theorem 
  • Random processes; the random process model, types of random processes, stationarity, autocorrelation.

Textbook: R.D. Yates and D.J. Goodman, Probability and Random Processes, John Wiley