| Course Code: CS1001H Course Name: Introduction to Probability Prerequisites: NIL Syllabus: Foundations of Probability: Sample space, Events, Axioms of probability; Conditional probability and independence, Bayes` theorem and applications; Random Variables: Discrete random variables, Probability mass function (PMF), Cumulative distribution function (CDF), Examples of discrete distributions; Continuous random variables, Probability density function (PDF), Examples of continuous distributions; Expectation, Variance, Conditional expectation; Jointly Distributed Random Variables: Joint distributions, Marginal distributions, Covariance and correlation coefficient; Limit Theorems and Inequalities: Markov `s inequality, Chebyshev `s inequality; Law of large numbers, Central limit theorem; Markov Chains: Transition matrices, Steady-state probabilities Texts: 1. H. Pishro-Nik, Introduction to Probability, Statistics and Random Processes, Kappa Research LLC, 2014. [Available at https://www.probabilitycourse.com ] 2. S. M. Ross, Introduction to Probability Models (12th Ed.), Academic Press, 2019 |