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# M3 Notes VTU 22 Scheme – Computer Science Maths Notes

VTU NOTES
Subject code
BCS301
Semester
3rd

## Module - 1

Probability Distributions 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. (12 Hours) (RBT Levels: L1, L2 and L3) Pedagogy Chalk and Board, Problem-based learning

## Module - 2

Joint probability distribution & Markov Chain 15.09.2023 14.09.2023 Annexure-II 2 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.