Course Details
Subject {L-T-P / C} : MA2001 : Probability and Statistics { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Suchandan Kayal
Syllabus
Module-I: Axioms of probability measure, Addition and multiplication theorems, Conditional probability, Bayes theorem, Independent events, Random variable, Discrete and continuous types of random variables, Cumulative distribution function (CDF), Probability mass function (PMF), Probability density function (PDF).
Module-II: Mean, Variance, Standard deviation, Moments, Skewness and kurtosis, Moment generating function, Binomial distribution, Poisson distribution, Hypergeometric distribution, Exponential distribution, Normal (Gaussian) distribution, Sampling (with and without replacement).
Module-III: Two dimensional random variables, Joint CDF, joint PDF/PMF, Marginal distribution, Conditional distribution.
Module-IV: Point estimation: Method of moments estimation, Method of maximum likelihood estimation, Confidence intervals for mean and variance in the case of normal distribution, Testing of hypothesis (parameters of normal distribution), Goodness of fit Chi-square test.
Module-V: Regression and correlation analysis, Rank correlation coefficient.
Course Objectives
- The undergraduate students will learn some basic probability and distribution theory. They will learn various inequalities regarding probabilities. A thorough knowledge of the concept of random variables will help them to understand the consequent sections. In the process, they will learn the probability density function and probability mass function.
- The students will learn how to compute the expectation, variance, median, quantile and generally the moments of a random variable or distribution. The students will learn various types of distributions, which are very important in real-life applications.
- The students will learn the definition of a two-dimensional random variable and its distribution and probability functions. They will learn to compute probabilities using a two-dimensional random variable.
- The students will learn some estimation methods, particularly point estimation and interval estimation for the unknown parameter. In point estimation, they will learn how to find the maximum likelihood estimator and method of moment estimator for an unknown parameter involved in a distribution. In the case of interval estimation, they will learn how to find interval estimators of mean and variance in the case of normal distribution. An introduction to hypothesis testing problems with error types will also be learned. The students will also learn the Chi-square method for fitting a distribution to real-life data, which will benefit them when they do certain project work on data analysis in the future during their internship program. <br /> <br />The students will learn linear regression and correlation analysis. In regression analysis, they will know how to predict a future value based on a linear regression curve using the least square technique. In correlation analysis, they will be taught regarding the linear dependency of two data sets. This will help them to know the level of linear dependency among the data. They will also know how to calculate the rank correlation coefficient between two datasets.
Course Outcomes
The students will be equipped with some basic knowledge of probability and statistics. In fact, this course will form the backbone of statistical analysis. After completing this course, they will be equipped with various statistical methods for estimating parameters, obtaining confidence intervals, and testing a hypothesis regarding an unknown parameter. Nowadays, statistical data analysis is one of the growing areas of research. Thus, students can make a career in higher studies. Moreover, the students will get better opportunities in terms of getting jobs and making their careers bright. This course will help them handle real-life problems that arise in various sectors, such as industry, medical science, engineering, economics, and many more.
Essential Reading
- V. K. Rohatgi & A.K. Md. Ehsanes Saleh,, An Introduction to Probability and Statistics, John Wiley and sons,
- Erwin Kreyszig, Advanced Engineering Mathematics, 10ed, ISV, Wiley
Supplementary Reading
- P. Billingsley,, Probability and Measure, John Wiley & Sons (SEA) Pvt. Ltd
- W. Feller, An introduction to probability theory and its applications, John Wiley and Sons