Specific Objectives of course:
A prime objective of the course is to introduce the students to the fundamentals of probability theory and present techniques and basic results of the theory and illustrate these concepts with applications. This course will also present the basic principles of random variables and random processes needed in applications.
Finite probability spaces:
Basic concept, probability and related frequency, combination of events, examples, Independence, Random variables, Expected value. Standard deviation and Chebyshev’s inequality. Independence of random variables. Multiplicativity of the expected value. Additivity of the variance, Discrete probability distribution.
Probability as a continuous set function:
sigma-algebras, examples. Continuous random variables, Expectation and variance. Normal random variables and continuous probability distribution.
de Moivre-Laplace limit theorem, weak and strong law of large numbers. The central limit theorem, Markov chains and continuous Markov process.