Semester- II Syllabus
B.Sc- I Year, II Semester (CBCS): Statistics
Syllabus
Paper-II: Probability Distributions (DSC-2B)
(4 HPW with 4 Credits and 100 Marks)
UNIT-I
Discrete
distributions – I : Uniform and Bernoulli distributions : definitions,
mean, variance and simple examples. Definition and derivation of probability
function of Binomial distribution, Poisson distribution definition, properties
of these distributions such as median, mode, m.g.f, c.g.f., p.g.f., c.f., and
moments up to fourth order, reproductive property, wherever exists, and their
real life applications. Poisson approximation to Binomial distribution.
UNIT-II
Discrete
distributions – II : Negative binomial, Geometric distributions :
Definitions and
physical
condition, properties of these distributions such as m.g.f, c.g.f., p.g.f.,
c.f. and moments up to fourth order, reproductive property, wherever exists,
lack of memory property for Geometric distribution and their real life applications.
Poisson approximation to Negative
binomial
distribution. Hyper-geometric distribution – definition, physical conditions, derivation
of probability function, mean, variance and real life applications. Binomial
approximation to Hyper-geometric.
UNIT-III
Continuous
distributions – I : Rectangular and Normal distributions – definition,
properties
such
as m.g.f., c.g.f., c.f. and moments up to fourth order, reproductive property,
wherever exists and their real life applications. Normal distribution as a
limiting case of Binomial and Poisson distributions.
UNIT-IV
Continuous
distributions – II : Exponential, Gamma : definition, properties such as
m.g.f., c.g.f., c.f. and moments up to fourth order, reproductive property
wherever exists and their real life applications. Beta distribution of two
kinds : Definitions, mean and variance. Cauchy distribution - Definition and
c.f.
Definition
of convergence in Law, in probability and with probability one or almost sure
convergence.
Definition of Weak Law of Large Numbers (WLLN) and Strong Law of Large
numbers
(SLLN). Definition of Central Limit Theorem (CLT) for identically and independently
distributed (i.i.d) random variables with finite variance.
Reference books:
Chand&Sons,
New Delhi
2. GoonAM,Gupta
MK,Das Gupta B : Fundamentals of Statistics , Vol-I, the World
Press
Pvt.Ltd., Kolakota.
3.
M.JaganMohan Rao and Papa Rao: A Text book of Statistics Paper-I.
Practical Paper – II
(With 2 HPW, Credits 1 and Marks 25)
1. Fitting of
Binomial distribution – Direct method.
2. Fitting of Binomial
distribution – Direct method using MS Excel.
3. Fitting of
binomial distribution – Recurrence relation Method.
4. Fitting of
Poisson distribution – Direct method.
5. Fitting of
Poisson distribution – Direct method using MS Excel.
6. Fitting of
Poisson distribution - Recurrence relation Method.
7. Fitting of
Negative Binomial distribution.
8. Fitting of
Geometric distribution.
9. Fitting of
Normal distribution – Areas method.
10. Fitting of
Normal distribution – Ordinates method.
11. Fitting of
Exponential distribution.
12. Fitting
of Exponential distribution using MS Excel.
13. Fitting of a
Cauchy distribution.
14. Fitting
of a Cauchy distribution using MS Excel.
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