Probability

Paper – I : Probability
UNIT – I

Random experiment, trial, sample point and sample space, events, operations of events,

concepts of equally likely, mutually exclusive and exhaustive events.
Definition of probability : Classical, relative frequency and axiomatic approaches. Discrete
probability space, properties of probability under set theoretic approach. Independence of
events , Conditional probability, total and compound probability theorems, Bayes theorem and
its applications.

UNIT – II

Random variables – discrete , cumulative and continuous, probability mass function (pmf) and probability density function (pdf), Cumulative distribution function (cdf) , Binomial Distribution function, Mixed Distributions , Joint distribution of two random variables, marginal and conditional distributions.

UNIT – III

Independence of random variables. Expectation of a random variable (rv) and its properties.,
expectation of sum of random variables and product of independent random variables,
conditional expectation.

UNIT – IV

Moments, moment generating function (m.g.f.) & their properties, continuity theorem for
m.g.f. (without proof).Chebyshev’s inequality. Weak law of large numbers and Central Limit
Theorem for a sequence of independently and identically distributed random variables and
their applications.