JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisites

Mathematics courses of first year of study.

Course Objectives:

• To understand the basic Number Theory concepts useful for computer organization and security, coding and cryptography.
• To understand the linear and multiple regression and correlation of the data, ANOVA
• To know the linear and nonlinear fitting of the given data.
• To understand the theory of probability distributions of single and multiple random variables
• To gain the knowledge of the sampling theory and testing of hypothesis and making inferences
• To understand the Stochastic process and Markov chains.

Course Outcomes

After learning the contents of this course, the student is able to

• Apply the concepts of number theory to cryptography domain.
• Find the quality and quantity of relationship among the given variables.
• Form the probability distribution of a random variable and Apply the concepts of probability distributions to some case studies
• Make inferences of the population (from which dada is taken) from the knowledge of the given data (testing of hypothesis)
• Understand the processes of functions of random variables

UNIT - I

Greatest Common Divisors and Prime Factorization: Greatest common divisors, The Euclidean algorithm, The fundamental theorem of arithmetic, Factorization of integers and the Fermat numbers Congruences: Introduction to congruences, Linear congruences, The Chinese remainder theorem, Systems of linear congruences

UNIT - II

Regression and Correlation: Linear Statistical Models (no derivations): Simple linear regression & correlation. Multiple regression & multiple correlation (three variables), Analysis of variance: one way, two way (no RBD, Latin square design). Fitting the linear and quadratic and exponential curves by the method of least squares to the given data. Random Variables and Probability Distributions: Concept of a Random Variable, Discrete Probability distributions, Continuous Probability Distributions, Statistical Independence. Discrete Probability Distributions: Binomial Distribution, Poisson distribution.

UNIT - III

Continuous Probability Distributions: Normal Distribution, Areas under the Normal Curve, Applications of the Normal Distribution, Normal Approximation to the Binomial distribution Fundamental Sampling Distributions: Random Sampling, Sampling Distributions, Sampling Distribution of Means and the Central Limit Theorem, Sampling Distribution of S2, t–Distribution, F- Distribution.

UNIT - IV

Estimation & Tests of Hypotheses: Introduction, Statistical Inference, Classical Methods of Estimation. Estimating the Mean, Standard Error of a Point Estimate, Prediction Intervals, Tolerance Limits, Estimating the Variance, Estimating a Proportion for single mean, Difference between Two Means, between Two Proportions for Two Samples and Maximum Likelihood Estimation.

UNIT - V

Stochastic Processes and Markov Chains: Introduction to Stochastic processes- Markov process. Transition Probability, Transition Probability Matrix, First order and Higher order Markov process, nstep transition probabilities, Markov chain, Steady state condition, Markov analysis.

TEXT BOOKS:

• 1. Kenneth H. Rosen, Elementary number theory & its applications, sixth edition, Addison-Wesley, ISBN 978 0-321-50031-1
• 2. Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye, Probability & Statistics for Engineers & Scientists, 9th Ed. Pearson Publishers.
• 3. S. D. Sharma, Operations Research, Kedarnath and Ramnath Publishers, Meerut, Delhi.

REFERENCE BOOK:

• 1. S C Gupta and V K Kapoor, Fundamentals of Mathematical statistics, Khanna publications.
• 2. T.T. Soong, Fundamentals of Probability and Statistics for Engineers, John Wiley & Sons Ltd, 2004.
• 3. Sheldon M Ross, Probability and statistics for Engineers and scientists, Academic Press.
• 4. N. Draper & H. Smith, Applied Regression Analysis Wiley Series in Probability and Statistics. Web References:
• 1) https://onlinecourses.nptel.ac.in/noc17_ch03/preview
• 2) https://www.edx.org/course/statistical-modeling-and-regression-analysis