Syllabus - Probability, Statistics and Linear Algebra (IS401)

CSE

Probability, Statistics and Linear Algebra (IS401)

IV

Unit 1

Basic Probability

Probability spaces, conditional probability, independence; Discrete random variables, continuous random variable and their properties, distribution functions and densities, exponential and gamma densities. Independent random variables, the multinomial distribution, Chebyshev's Inequality, Bayes' rule.

Unit 2

Basic Statistics

Measures of Central tendency: Moments, skewness and Kurtosis - Probability distributions: Binomial, Poisson and Normal - evaluation of statistical parameters for these three distributions, Correlation and regression – Rank correlation.

Unit 3

Applied Statistics

Curve fitting by the method of least squares- fitting of straight lines, second degree parabolas and more general curves. Test of significance: Large sample test for single proportion, difference of proportions, single mean, difference of means, and difference of standard deviations.

Unit 4

Small samples

Test for single mean, difference of means and correlation coefficients, test for ratio of variances – Testing of Hypothesis and independence of attributes, Time Series

Unit 5

Linear Algebra

Cramer's rule, Singular Value decomposition, Euclidian vector spaces, Projection. Hermitian and Unitary Matrix, Gram -Schmidt orthogonalization, LU- decomposition

Practicals

Reference Books

  • ErwinKreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, 2006.

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

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

  • W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd Ed., Wiley, 1968.

  • N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications, Reprint, 2010.

  • B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition, 2000.

  • Veerarajan T., Engineering Mathematics (for semester III), Tata McGraw-Hill, New Delhi, 2010.

  • Mathematics For Machine Learning-Marc Peter Deisenroth,A. Aldo Faisal,Cheng soon ong