Random Experiment; Sample space; Random Events; Probability of events. Axiomatic definition of
probability; Frequency Definition of probability; Finite sample spaces and equiprobable measure as
special cases; Probability of Non-disjoint events (Theorems). Counting techniques applied to
probability problems; Conditional probability; General Multiplication Theorem; Independent
events; Bayes’ theorem and related problems.
Random variables (discrete and continuous); Probability mass function; Probability density
function and distribution function. Distributions: Binomial, Poisson, Uniform, Exponential,
Normal, t and χ2. Expectation and Variance (t and χ2 excluded); Moment generating function;
Reproductive Property of Binomal; Poisson and Normal Distribution (proof not required).
Transformation of random variables (One variable); Chebychev inequality (statement) and
problems.
Binomial approximation to Poisson distribution and Binomial approximation to Normal distribution
(statement only); Central Limit Theorem (statement); Law of large numbers (Weak law); Simple
applications.