Algebra of sets, introduction to probability, random variables, probability distributions, moments, moment generating function, Markov and Chebyshev inequalities, special discrete and continuous distributions, the function of a random variable, joint distributions, bivariate normal distribution, transformation of random vectors, central limit theorem, sampling distributions, 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, testing of hypotheses, Neyman-Pearson lemma, tests for one sample and two sample problems for normal populations.

The students will be equipped with a foundation in probability and statistics. They will learn many statistical methodologies that can be useful in data analysis in engineering, physics, biological science, finance, actuarial science, etc. Having a thorough knowledge of the course, one can easily make a career in statistics in future. The objective of this course is to equip students with the fundamental knowledge of probabilistic and statistical analysis, which can be used in various applications in engineering and
science like modelling practical datasets, weather prediction and computer networks.

The students will be learning many statistical methods which can be used for solving some real-life problems using statistical tools

The students will be learning statistical inference, which is one of the most interesting research areas in statistics. In future, students can choose a career in statistics, which is very demanding.

The students can frame a statistical hypothesis and make inferences regarding the population. In many real-life situations, the statistical hypothesis can solve the problem.

After completion of this subject, a student will be able to do the following.

1. Analyze statistical data graphically using frequency distributions and
cumulative frequency distributions.

2. Translate real-world problems into probability models

3. Demonstrate an understanding of the theory of maximum likelihood
estimation.

4. Employee the principles of linear regression and correlation, including
least square method, predicting a particular value of Y for a given value
of X and the significance of the correlation coefficient.

5. Use the normal probability distribution, including the standard normal curve
calculations of appropriate areas.

6 Identify the characteristics of different discrete and continuous
distributions. Identify the type of statistical situation to which different distributions
can be applied.

V. K. Rohatagi and A.K. Md. E. Saleh, An Introduction to Probability and Statistics, John Wiley and sons, 2001

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

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

J. S. Milton and J.C. Arnold, Introduction to Probability and Statistics, McGraw Hill