GAYATRI VIDYA
PARISHAD COLLEGE FOR DEGREE AND P.G. COURSES (A)
DEPARTMENT OF
STATISTICS
PROPOSED SYLLABUS
FOR SECOND SEMESTER
With Effected
From 2020-21
Paper-II: Probability Theory and Distributions
|
Assessment |
Internal |
External |
Total |
No. of Hrs
per Week |
Credits |
|
Theory (Marks) |
25 |
75 |
100 |
4 |
4 |
|
Practical
(Marks) |
Internal
& External |
50 |
2 |
1 |
|
Course Objectives:
This paper deals with
the situation where there is uncertainty and how to measure that uncertainty by
defining the probability, random variable and mathematical expectation which
are essential in all research areas. This
paper gives an idea of using various standard theoretical distributions, their
chief characteristics and applications in analyzing any data.
Unit-I (11 hours) [CO1]
Introduction to Probability: Basic Concepts of Probability, random experiments, trial, outcome,
sample space, event, mutually exclusive and exhaustive events, equally likely
and favourable outcomes. Mathematical, Statistical, axiomatic definitions of
probability. Conditional Probability and independence of events, Addition and
multiplication theorems of probability for 2 and for n events. Boole's
inequality and Baye's theorem and its applications in real life problems.
Unit-II (12
hours)[CO2]
Unit-III (12
hours)[CO3]
Unit-IV (12 hours)[CO4]
Unit – V (11 hours) [CO5]
Continuous Distributions:
Rectangular, Exponential, Gamma, Beta Distributions: mean , variance, M.G.F,
C.G.F, C.F. Normal Distribution:
Definition, Importance, Properties, M.G.F, CF, additive property.
Text Books:
1. V.K.Kapoor
and S.C.Gupta: Fundamentals of
MathematicalStatistics,Sultan Chand & Sons, NewDelhi.
2 BA/BSc I year statistics -
descriptive statistics, probability distribution - Telugu Academy
- Dr M.JaganmohanRao,DrN.Srinivasa
Rao, Dr P.Tirupathi Rao, Smt.D.Vijayalakshmi.
3. K.V.S. Sarma:
Statistics Made Simple: Do it yourself on PC. PHI
Reference books:
1.
Willam
Feller: Introduction to Probability theory and its applications. Volume
–I,Wiley
2.
Goon
AM, Gupta MK, Das Gupta B : Fundamentals of Statistics , Vol-I, the World Press Pvt.Ltd.,Kolakota.
3.
Hoel
P.G: Introduction to mathematical statistics, Asia Publishinghouse.
4.
M.
JaganMohan Rao and Papa Rao: A Text book of StatisticsPaper-I.
5.
Sanjay
Arora and Bansi Lal: New Mathematical Statistics: Satya Prakashan , NewDelhi
6.
Hogg
Tanis Rao: Probability and Statistical Inference. 7th edition. Pearson.
Practicals - Semester – II
1.
Fitting
of Binomial distribution – Direct method.
2.
Fitting
of binomial distribution – Recurrence relation Method.
3.
Fitting
of Poisson distribution – Direct method.
4.
Fitting
of Poisson distribution - Recurrence relation Method.
5.
Fitting
of Negative Binomial distribution.
6.
Fitting
of Geometric distribution.
7.
Fitting
of Normal distribution – Areas method.
8.
Fitting
of Normal distribution – Ordinates method.
9.
Fitting
of Exponential distribution.
Note: Training
shall be on establishing formulae in Excel and derive the results. The Excel
output shall be exported to M.S. Word for writing inference.
Course Outcomes:
1)
Ability to distinguish between random and
non-random experiments,
2) Knowledge to conceptualize the probabilities of
events including frequentist and axiomatic approach.
Simultaneously, they will learn the notion of conditional probability including
the concept of Bayes’ Theorem,
3) Knowledge related to concept of discrete and
continuous random variables and their probability
distributions including expectation and moments,
4) Knowledge of important discrete and continuous
distributions such as Binomial, Poisson, Geometric,
Negative Binomial and Hyper-geometric, normal, uniform, exponential, beta and
gamma distributions,
5) Acumen
to apply standard discrete and continuous probability distributions to
different situations.
