Probability Classical & Axiomatic Definition of Probability Law of total probability Conditional probability Bayes’ theorem and applications Discrete and continuous random variables Standard discrete & continuous probability distributions Modes of convergences Mathematical expectation and conditional expectation Inversion, uniqueness and continuity theorems Borel 0-1 law, Kolmogorov’s 0-1 law Tchebycheff’s and Kolmogorov’s inequalities Laws of large numbers & central limit theorems Statistical Methods Collection, compilation & presentation of data/charts/diagrams/histogram Frequency distribution Measures of location/dispersion/skewness/kurtosis Bivariate and multivariate data Association and contingency Curve fitting and orthogonal polynomials Bivariate normal distribution Regression-linear, polynomial Correlation coefficient Partial and multiple correlation Intraclass correlation Correlation ratio Standard errors & large sample test Sampling distributions of sample mean Non-parametric tests Order statistics Concept of Asymptotic relative efficiency Numerical Analysis Finite differences of different orders Concept of interpolation and extrapolation Inverse interpolation Numerical differentiation Summation of Series Numerical solutions of differential equations Computer application & Data Processing Basics of Computer Operations of a computer Different units of a computer system Output and peripheral devices Software, system and application software, Operating systems Low and High level languages RAM, ROM, unit of computer memory Network – LAN, WAN, internet, intranet Basics of computer security Basics of Programming |