Module 1: Algebra of sets, introduction to probability (various definitions of probability), random variables (types of random variables), probability distributions.

Module 2: Moments, probability generating function, moment generating function, Markov and Chebyshev inequalities, special discrete and continuous distributions.

Module 3: Function of a random variable, joint distributions, bivariate normal distribution, transformation of random vectors, central limit theorem, sampling distributions,

Module 4: Point estimation, unbiasedness, consistency, method of moments and maximum likelihood estimation, confidence intervals for parameters in one sample and two sample problems from normal populations.

Module 5: Testing of hypotheses, types of hypothesis and errors, Neyman-Pearson lemma, tests for one sample and two sample problems for normal populations.

To introduce the basic concept of probability and solve some related problems.

To introduce the concept of random variables for one and multidimensional (both discrete and continuous). To understand the cumulative distribution function, probability distribution.

To study the function of a random variable and its distribution. Characterization of distribution through moment generating function.

To introduce the concept of testing the hypotheses, Neyman-Pearson lemma, tests for one sample and two sample problems for normal populations.

CO1: The students will learn to compute probability for various types of events arising in practice.

CO2: The students will learn various types of random variables and their distribution. Further, they will learn the application of random variables in real-life situations, that is, the study of special types of distributions that have applications in real-life situations.

CO3: The students will learn the concept of characterization of a distribution function.

CO4: The students will learn the application of the central limit theorem and understand the importance of normal distribution.

CO5: The students will learn the concept of point and interval estimation of parameters. Also, learn how to compute these and study various properties of estimators.

CO6: Students will learn the method of hypothesis testing and various types of errors associated with hypothesis testing.

V. K. Rohatgi & A.K. Md. Ehsanes Saleh, , An Introduction to Probability and Statistics, John Wiley and sons

H. J. Larson, Introduction to Probability Theory and Statistical Inference, John Wiley & Sons

S. M. Ross, A First Course in Probability, Pearson publisher

W. Feller, An Introduction To Probability Theory & Its Applications, John Wiley & Sons