Code: BSc-104
Mathematics-II: probability and statistics
Credits : 4

Basis of statistics
Unit 1
Module 1: basic probability:
Probability spaces, conditional probability, independence; discrete random variables, independent random variables, the multi normal distribution, poison approximation to the binomial distribution, infinite sequences of Bernoulli trials, sums of independent random variables: expectation of discrete random variables, moments, variance of a sum, correlation coefficient, chebyshev's inequality.

Unit 2
Module 2: continuous probability distributions:
Continuous random variables and their properties, distribution functions and densities, normal exponential and gamma densities.

Module 3: bivariate distributions:
Bivariate distributions and their properties, distribution of sums and quotients, conditional densities, Bayes; rule.

Unit 3
Module 4: basic statistics:
Measures of Central tendency: moments, skewness and kurtosis- probability distributions: binomial, poison and normal- evaluation of statistical parameters for these three distributions, correlation and regression- rank correlation.

Module 5: applied statistics:
Curve fitting by the method of least squares- fitting of straight lines, second degree parabola and more general curves.

Unit 4
Applied statistics: test of significance: large sample test for single proportion, difference of proportions, single mean, difference of means, and difference of standard deviations.

Module 6: small samples:
Test for single mean, difference of means and correlation coefficients, test for ratio of variances- chi square test for goodness of fit and independence of attributes

Suggested text/reference books

1) Erwin Kreyszig, advanced engineering mathematics, 9th edition, John wiley and sons 2006.
2) P.G. Hotel, S.C. Port and C.J. Stone, introduction to probability theory, universal Book stall, 2003
3) S. Ross. A first course in probability, 6 th edition , Pearson education India, 2002.
4) W.Feller, an introduction to probability theory and its application, vol I, third edition wiley, 1968.
5) N.P. Bali and Manish Goyal, a textbook of engineering mathematics, Lakshmi publications,
6) B.S. Grewal, higher engineering mathematics, Khanna publishers, 35th edition 2000.
7) Veerarjan T.. Engineering mathematics (4 semester III), Tata mcgraw hill, New Delhi