 # JNTUH R18 B.Tech Mathematical And Statistical Foundations Syllabus 2022

Mathematical and Statistical Foundations Syllabus along with Course Objectives and Course outcome and list of textbook and reference books is mentioned in this blog. The subject of Mathematical and Statistical Foundations  has 5 units in total.

Topic and sub-topics of Mathematical and Statistical Foundations are mentioned below in detail. If you have any problem in understanding Mathematical and Statistical Foundations any other Engineering Subject in any semester or in any year then you can view the video lectures on the official CynoHub app.

## Mathematical and Statistical Foundations Syllabus Unit 1

### 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.

## Mathematical and Statistical Foundations Syllabus Unit 2

### Simple Linear Regression and Correlation:

Introduction to Linear Regression, The Simple Linear Regression Model, Least Squares and the Fitted Model, Properties of the Least Squares Estimators, Inferences Concerning the Regression Coefficients, Prediction, Simple Linear Regression Case Study.

### 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.

## Mathematical and Statistical Foundations Syllabus Unit 3

### Continuous Probability Distributions:

Normal Distribution, Areas under the Normal Curve, Applications of the Normal Distribution, Normal Approximation to the Binomial.

### Fundamental Sampling Distributions:

Random Sampling, Sampling Distributions, Sampling Distribution of Means and the Central Limit Theorem, Sampling Distribution of S2, t–Distribution, F- Distribution.

## Mathematical and Statistical Foundations Syllabus Unit 4

### 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.

## Mathematical and Statistical Foundations Syllabus Unit 5

### 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.

## Mathematical and Statistical Foundations course objectives:

• The Number Theory basic concepts useful for cryptography etc
• The theory of Probability, and probability distributions of single and multiple random variables
• The sampling theory and testing of hypothesis and making inferences
• Stochastic process and Markov chains.

## Mathematical and Statistical Foundations course outcomes:

After learning the contents of this course, the student must be able to

• Apply the number theory concepts to cryptography domain
• Apply the concepts of probability and distributions to some case studies
• Correlate the material of one unit to the material in other units
• Resolve the potential misconceptions and hazards in each topic of study.
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## Mathematical and Statistical Foundations reference books:

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

## Scoring Marks in Mathematical and Statistical Foundations Syllabus

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JNTUA B.tech R20 Mathematical and Statistical Foundations Syllabus was made clear in this article. To know about the syllabus of other Engineering Subjects of JNTUA check out the official CynoHub application. Click below to download the CynoHub application