BCS301 Mathematics for Computer Science
Course Learning Objectives
CLO 1. To introduce the concept of random variables, probability distributions, specific discrete and continuous distributions with practical application in Computer Science Engineering and social life situations.
CLO 2. To Provide the principles of statistical inferences and the basics of hypothesis testing with emphasis on some commonly encountered hypotheses.
CLO 3. To Determine whether an input has a statistically significant effect on the system’s
response through ANOVA testing.
SYLLABUS COPY
MODULE - 1
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 distributions- problems (derivations for mean and standard deviation for Binomial and Poisson distributions only)-Illustrative examples. Exponential distribution.
MODULE - 2
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 and absorbing states.
MODULE - 3
Statistical Inference 1: Introduction, sampling distribution, standard error, testing of hypothesis, levels of significance, test of significances, confidence limits, simple sampling of attributes, test of significance for large samples, comparison of large samples.
MODULE - 4
Statistical Inference 2: Sampling variables, central limit theorem and confidences limit for unknown mean. Test of Significance for means of two small samples, students ‘t’ distribution, Chi-square distribution as a test of goodness of fit. F-Distribution.
MODULE - 5
Design of Experiments & ANOVA: Principles of experimentation in design, Analysis of completely randomized design,
randomized block design. The ANOVA Technique, Basic Principle of ANOVA, One-way
ANOVA, Two-way ANOVA, Latin-square Design, and Analysis of Co-Variance.
Course outcome
At the end of the course the student will be able to:
CO 1. Explain the basic concepts of probability, random variables, probability distribution
CO 2. Apply suitable probability distribution models for the given scenario.
CO 3. Apply the notion of a discrete-time Markov chain and n-step transition probabilities to
solve the given problem
CO 4. Use statistical methodology and tools in the engineering problem-solving process.
CO 5. Compute the confidence intervals for the mean of the population. CO 6. Apply the ANOVA test related to engineering problems.
Suggested Learning Resources
Text Books
1. Ronald E. Walpole, Raymond H Myers, Sharon L Myers & Keying Ye “Probability &
Statistics for Engineers & Scientists”, Pearson Education, 9th edition, 2017.
2. Peter Bruce, Andrew Bruce & Peter Gedeck “Practical Statistics for Data Scientists” O’Reilly Media, Inc., 2nd edition 2020.
Reference:
1. Erwin Kreyszig, “Advanced Engineering Mathematics”, John Wiley & Sons, 9th Edition, 2006.
2. B. S. Grewal “Higher Engineering Mathematics”, Khanna publishers, 44th Ed., 2021.
3. G Haribaskaran “Probability, Queuing Theory & Reliability Engineering”, Laxmi Publication, Latest Edition, 2006
4. Irwin Miller & Marylees Miller, John E. Freund’s “Mathematical Statistics with Applications” Pearson. Dorling Kindersley Pvt. Ltd. India, 8th edition, 2014.
5. S C Gupta and V K Kapoor, “Fundamentals of Mathematical Statistics”, S Chand and Company, Latest edition.
6. Robert V. Hogg, Joseph W. McKean & Allen T. Craig. “Introduction to Mathematical Statistics”, Pearson Education 7th edition, 2013.
7. Jim Pitman. Probability, Springer-Verlag, 1993.
8. Sheldon M. Ross, “Introduction to Probability Models” 11th edition. Elsevier, 2014.
9. A. M. Yaglom and I. M. Yaglom, “Probability and Information”. D. Reidel Publishing
Company. Distributed by Hindustan Publishing Corporation (India) Delhi, 1983.
10. P. G. Hoel, S. C. Port and C. J. Stone, “Introduction to Probability Theory”, Universal Book Stall, (Reprint), 2003.
11. S. Ross, “A First Course in Probability”, Pearson Education India, 6th Ed., 2002.
12. W. Feller, “An Introduction to Probability Theory and its Applications”, Vol. 1, Wiley, 3rd