Mumbai University

APPLIED MATHEMATICS V

APPLIED MATHEMATICS V

Probability and topics in Statistics: Statistical experiments with random outcomes, Sample space, probability defined on the basis of sample space and on the basis of events and their combinations. Theorem on probabilities, conditional probability. Bayes theorem. Random variable, probability distribution for discrete and continuous random variables. Density function and distribution functions. Expected values, variance , moments, moment generating functions, Bernoulli’s trials, Binomial , Poisson, normal distributions for detailed study with proof, Other common distributions, T , F, Beta, Gamma, X with indication of the applications(without proof) Central limit theorem, Bivariate probability and frequency distributions, Correlations, regression, lines of regression. Introduction to random samples, use of random numbers, stochastic processes, Time series , queuing theory.

Optimisation Techniques

· Problem formulation

· Simplex Method

· Revised Simplex Method

· Duality & Sensivity

· Unconstrained optimisation of several variables

· Numerical methods for unconstrained optimisation : Random search & Univariate method, Fletcher Reverse method, Newtons method

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