Core course for B.Sc. (Research) Mathematics, Economics.

**Credits (Lec:Tut:Lab)**= 3:1:0 (3 lectures and 1 tutorial weekly)

**Prerequisites: **Any one of Calculus I (MAT 101) or Elementary Calculus (MAT 020) or Mathematical Methods I (MAT 103) or Basic Probability & Statistics (MAT 084)

**Overview**: Probability is the means by which we model the inherent randomness of natural phenomena. This course introduces you to a range of techniques for understanding randomness and variability, and for understanding relationships between quantities. The concluding portions on Statistics take up the problem of testing our theoretical models against actual data, as well as applying the models to data in order to make decisions. This course is a prerequisite for later courses in Advanced Statistics, Stochastic Processes, and Mathematical Finance, as well as for the Minor in Data Analytics.

**Detailed Syllabus:**

**Probability:**Classical probability, axiomatic approach, conditional probability, independent events, addition and multiplication theorems with applications, Bayes’ theorem.**Random Variables**: Probability mass function, probability density function, cumulative density function, expectation, variance, standard deviation, mode, median, moment generating function.**Some Distributions and their Applications:**Uniform (discrete and continuous), Bernoulli, Binomial, Poisson, Exponential, Normal.**Joint Distributions:**Joint and marginal distributions, independent random variables, IIDs, conditional distributions, covariance, correlation, moment generating function.**Sequences of Random Variables:**Markov’s Inequality, Chebyshev’s Inequality, Law of Large Numbers, Central Limit Theorem.

**References:**

*A First Course in Probability*by Sheldon Ross, 6^{th}edition, Pearson.*Introduction to Probability and Statistics for Engineers and Scientists*by Sheldon Ross, 2nd edition, Harcourt Academic Press.*Theory and Problems of Probability and Statistics*by Murray R Spiegel and Ray Meddis, Schaum’s Outlines.*John E. Freund’s Mathematical Statistics with Applications*by I. Miller & M. Miller, 7^{th}edition, Pearson, 2011.*Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance*by Kai Lai Chung and Farid Aitsahlia, 4^{th}edition, Springer International Edition, 2004.

**Past Instructors**: Debashish Bose, Suma Ghosh