Syllabus: Geometric, Negative binomial, Hyper-Geometric, exponential, Gamma and Beta distributions, Chi-square distributions, and their applications. Relationships between distributions. Two and Higher-Dimensional Random Variables: Joint cumulative distribution function, joint probability density function, marginal and conditional densities, independence, Multinomial distribution, bi-variate normal distribution, covariance, correlation coefficient. Conditional expectation, expectation of functions of random variables, cumulative distribution function technique, moment generating function. Functional relationships between distributions and their uses in statistical inference. Transformation of random variables , derivation of t and F distribution, characteristic functions. Limiting distributions, the weak law of large numbers, Central Limit theorem

Syllabus: PART A – INTRODUCTION TO STATISTICS Descriptive Statistics: Types of data (qualitative, quantitative, discrete, continuous), data summarization, frequency table, cumulative frequency table, histogram, bar chart, pie chart percentiles, quartiles, measures of location (mean, median, mode). Measures of dispersion (range, Std. Deviation), coefficient of variation, skew ness kurtosis. Probability: Introduction, frequency definition; classical definition, axiomatic definition, finite sample spaces, equally likely events, mutually exclusive events, conditional probability, theorem of total probabilities, Baye’s theorem, tree diagram, independent events. One –Dimensional Random Variables and Probability Density Functions: Random variables, probability density function, cumulative distribution functions, expected value, variance, associated theorems, various Generating functions, and distribution of functions of random variables. Discrete Distributions: Uniform Bernoulli, Binomial, Poisson process and Poisson distributions, and their applications. Continuous Distributions: Uniform, Normal distributions, the Central Limit Theorem and its applications. PART B – MATHEMATICS FOR COMPUTING Sets and relations , Cartesian products of sets, relations as subsets of Cartesian products, partitions, coverings, permutations, combinations, functions and mappings, relations and their properties including symmetry, transitivity and functionality; logical operators, Venn diagrams; Boolean algebra, truth tables, normal forms, propositional connectives, tautologies and contradictions, simple propositional calculus using natural deduction method, validity of arguments, rules of inference, conditional proof and method of reducio ad absurdum, syntax and semantics, first order predicate logic: symbols, terms, theorems, first order calculi: natural deduction, correctness and completeness.

Evaluation Criteria: Inclass and take home assignments are consider here.