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.