#### 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.

#### Applications:

de Moivre-Laplace limit theorem, weak and strong law of large numbers. The central  limit  theorem,  Markov  chains  and  continuous  Markov process.