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,
Bernoullis 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.
Introduction to Discrete Structures :
Mathematical logic, prepositions, statement and negation, combinations of
statements, their truth tables, logical equivalence.
Operations on sets, relations and their functions, partial order and equivalence relations, Peanos axioms and mathematical induction, Injective, Surjective, Bijective functions, Pigeonhole principle and its applications. Formal mathematical systems, elements of theory of some algebras such as rings, integral domains, group, fields Boolean algebra, semigroup.
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