Mathematics – IIA (BS-M201)
6 units: Basic Probability, Continuous Probability Distributions, Bivariate Distributions, Basic Statistics, Applied Statistics · L-T-P 3L+1T/week.
Detailed syllabus
Unit 1: Basic Probability (11 hours)
Basic Probability: Probability spaces, conditional probability, independence; Discrete random variables, Independent random variables, the Multinomial distribution, Poisson 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: Continuous Probability Distributions (4 hours)
Continuous Probability Distributions: Continuous random variables and their properties, Distribution functions and densities, Normal, Exponential and Gamma densities.
Unit 3: Bivariate Distributions (5 hours)
Bivariate Distributions: Bivariate distributions and their properties, distribution of sums and quotients, Conditional densities, Bayes' rule.
Unit 4: Basic Statistics (8 hours)
Basic Statistics: Measures of Central tendency, Moments, Skewness and Kurtosis, Probability distributions: Binomial, Poisson and Normal and evaluation of statistical parameters for these three distributions, Correlation and regression – Rank correlation
Unit 5: Applied Statistics (8 hours)
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 6: Small samples (4 hours)
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.
Source: official document