Probability, Distributions and Statistics (1BMATCS301)

Probability, Distributions and Statistics

Course Code 1BMATCS301 
Scheme 2025
Type of Course ASC 
Semester 3
Teaching Hours/Week (L:T:P) 3:2:0 
CIE Marks 50
Total Hours of Pedagogy per semester L :T:P:SL&TW:TH
42:28:0:50:120 
SEE Marks 50
Credits 4 
Total Marks 100
Examination type (SEE) Theory 
Exam Hours 03

Module-1: Modular Arithmetic

Introduction of modular arithmetic and its applications in Computer Science and Engineering. Introduction to Congruences, Linear Congruences, The Remainder theorem, Solving Polynomials, Linear Diophantine Equation, System of Linear Congruences, Euler’s Theorem, Wilson Theorem and Fermat’s little theorem. Applications of Congruences-RSA algorithm.

Module-2: Statistics

Principles of least squares, Curve fitting by the method of least squares in the form: 𝑦 = 𝑎 + 𝑏𝑥 , 𝑦 = 𝑎 + 𝑏𝑥 + 𝑐𝑥2 , and 𝑦 = 𝑎𝑥𝑏 . Correlation, Coefficient of correlation, Lines of regression, Angle between regression lines, rank correlation.

Module-3: Probability Distributions

Review of basic probability theory. Random variables (discrete and continuous), probability mass and density functions. Mathematical expectation: mean and variance. Binomial, Poisson and normal distributionsproblems (derivations for mean and standard deviation for Binomial and Poisson distributions only).

Module-4: Joint probability distribution

Joint Probability distribution for two discrete random variables, expectation, covariance and correlation. Markov Chain: Introduction to Stochastic Process, Probability Vectors, Stochastic matrices, Regular stochastic matrices, Markov chains, Higher transition probabilities, Stationary distribution of Regular Markov chains.

Module-5: Statistical Inference

Sampling distribution, standard error. Levels of significance. Testing of hypothesis. Test of significances. Confidence limits, simple sampling of attributes. Sampling variables, central limit theorem and confidences limit for unknown mean.

Test of significance for large samples (mean, proportion). Comparison of large samples (mean, proportion).

Test of Significance for means of two small samples, students-‘t’ distribution, and Chi-square distribution as a test of goodness of fit.

TUTORIAL COMPONENT OF PCC

Tutorial Topic/Problem solving/Case … etc. (for 2 hours each): 

1. Practice problems on linear congruences

2. Practice Problems on Linear Diophantine Equation, System of Linear Congruences

3. Practice problems on Euler’s Theorem, Wilson Theorem and Fermat’s little theorem.

4. Practice problems on fitting linear form and quadratic form

5. Practice problems on 𝑦 = 𝑎𝑥𝑏 and correlation

6. Practice problems on lines of regression and rank correlation

7. Practice problems on mathematical expectations

8. Practice problems on Binomial and Poisson distributions

9. Practice Problems on Normal distributions

10. Practice problems on covariance, correlation of two discrete random variables

11. Practice problems on Markov chain, stochastic matrices, probability vectors

12. Practice Problems on higher transition probabilities and stationary distributions

13. Practice Problems on test of significance for large samples

14. Practice problems on test of significance for small samples

Suggested Learning Resources: 

Textbooks:

1. Ronald E. Walpole, Raymond H Myers, Sharon L Myers & Keying Ye “Probability and Statistics for Engineers and Scientists”, Pearson Education, 9th edition, 2012.

2. Murray R. Spiegel, Larry J. Stephens, Statistics, Schaum’s outline series, 6th edition,

3. Koshy, Thomas. Elementary number theory with applications. Academic press, 2nd Edition, 2009.

4. Seymour Lipschutz and Marc Lars Lipson, Probability, Schaum’s Outline Series, Second edition, 2011.

Reference books / Manuals:

1. Erwin Kreyszig, “Advanced Engineering Mathematics”, John Wiley & Sons, 11 th Edition, 2006.

2. B. S. Grewal “Higher Engineering Mathematics”, Khanna publishers, 45 th Ed., 2021.

3. Irwin Miller & Marylees Miller, John E. Freund’s “Mathematical Statistics with Applications” Pearson. Dorling Kindersley Pvt. Ltd. India, 8th edition, 2014.

4. S C Gupta and V K Kapoor, “Fundamentals of Mathematical Statistics”, S Chand and Company, 12th edition.

5. P. G. Hoel, S. C. Port and C. J. Stone, “Introduction to Probability Theory”, Universal Book Stall, (Reprint), 2003.

6. S. Ross, “A First Course in Probability”, Pearson Education India, 6th Ed., 2002.

7. David M Burton: “Elementary Number Theory” Mc Graw Hill, 7th Ed.,2017