Elements of set theory-Fundamentals of set, operations with set, laws of set, Venn diagram, review of permutation and combination, Binomial theorem, exponential and logarithmic series.
Probability-Probability and possibility, methods of assigning probabilities: classical, empirical, geometric, relative frequency and axiomatic methods of probability, probability measures and probability space, total probability, marginal and conditional probability, random experiment, sample space, events, event space, different types of events (mutually exclusive, exhaustive, independent events), tree diagrams, compound probability, Bayes theorem.
Random Variable-Concept of random variable, discrete and continuous random variables, probability mass function, probability density function, distribution function, function of random variable and its distribution, joint, marginal and conditional distributions, independence of random variables, set function, odds ratio.
Expectation-Meaning of expectation, marginal and conditional expectation, mean, variance, conditional mean and conditional variance, moments, covariance and correlation coefficient, expectation of sums and products of random variables, Chebyshev’s inequality.
Generating Function-Moment generating function, characteristic function, probability generating function, cumulant generating function and their properties, generating function and their applications in well known probability distribution.
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