Probability

SYLLABUS- PROBABILITY 1.1, B.Sc I Year – Paper I
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 and continuous, probability mass function (pmf)
and probability density function (pdf), Cumulative distribution function (cdf). 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 and related problems.
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.
B.Sc I Year – Paper II
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 and continuous, probability mass function (pmf)
and probability density function (pdf), Cumulative distribution function (cdf). 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 and related problems.
Unit– IV: Moments, moment generating function (m.g.f.) & their properties, continuity
theorem for m.g.f. (without proof). Cumulants and c.g.f., characteristics function
(definition only). 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 (statement only).