1
UNIVERSITY OF MUMBAI
Syllabus for the S.Y.B.A.
Program: B.A.
Course :STATISTICS
(Choice Based Credit Grading Semester System
with effect from the academic year 2017–2018)
2
S.Y.B.A. STATISTICS Syllabus
for C hoice Based Credit G rading Semester System
To be implemented from the Academic year 2017 -2018
Student must have passed 12th standard with mathematics. If not then he/she has to complete
the required bridge course.
SEMESTER II I
Course Code UNIT TOPICS Credits L / Week
UAST 301 I Elementary Probability Theory :
2 1
II Concept of Discrete random
variable and properties of its
probability distribution
1
III Some Standard Discrete
Distributions 1
UAST 30 2 I Linear Programming Problem (L.P.P.)
2 1
II Transportation Problem 1
III Assignment Problem and
Sequencing
1
UASTP3 Practicals based on both courses in theory 2 6
UASTP3
UASTP3(A)
UASTP3(B)
Practicals based on UAST301
Practicals based on UAST302
1
1
6
3
3
3
SEMESTER IV
Course Code UNIT TOPICS Credits L / Week
UAST 401 I Continuous random variable
2 1
II Some Standard Continuous
Distributions 1
III Elementary topics on Estimation
and Testing of hypothesis 1
UAST 40 2 I CPM and PERT
2 1
II Game Theory 1
III Decision Theory 1
UASTP4 Practicals based on both courses in theory 2 6
UASTP4
UASTP4(A)
UASTP4(B)
Practicals based on UAST401
Practicals based on UAST402
1
1
6
3
3
4
SEMESTER II I
Course Code Title Credits
UAST 301 STATISTICAL METHODS -1
2 Credits
(45 lectures )
Unit I: Elementary Probability Theory :
Trial, random experiment, sample point and sample space.
Definition of an event. Operation of events, mutually exclusive and exhaustive events.
Classical (Mathematical) and Empirical definitions of P robability and their properties .
Axiomatic definition of probability.
Theorems on Addition and Multiplication of probabilities , pair wise .(with proof)
Independence of events and mutual independence for three -events. Conditional
probability, Bayes’ theorem (with proof) and its applications.
15 Lectures
Unit II : Concept of Discrete random variable and properties of its probability
distribution:
Random variable. Definition and properties of probability distribution and
cumulative distribution function of discrete random variable.
Raw and Central moments (definition only) and their relationship. (upto order four
without proof ).
Concepts of Skewness and Kurtosis and their uses .
Expectation of a random variable. Theorems on Expectation and Variance. (with proof)
Joint probability mass function of two discrete random variables.
Marginal and conditional distributions.
Covariance and Coefficient of Correlation. Independence of two random variables.
15 Lectures
Unit III : Some Standard Discrete Distributions:
Discrete Uniform, Binomial and Poisson distributions and derivation of their mean and variance.
Recurrence relation for probabilities of Binomial and Poisson distributions a nd its
applications (with derivations) .
Poisson approximation to Binomial distribution (Statement only).
Hyper geometric distribution, Derivation of its mean and variance.
Binomial approximation to hyper geometric distribution (statement only)
15 Lectures
REFERENCES .
1. Medhi J. : Statistical Methods, An Introductory Text, Second Edition,
New Age International Ltd.
2 Agarwal B.L. : Basic Statistics, New Age International Ltd.
3. Spiegel M.R. : Theory and Problems of Statistics, Schaum’ s Publications series.
5
Tata McGraw -Hill.
4. David S. : Elementary Probability, Cambridge University Press.
5. Hoel P.G. : Introduction to Mathematical Statistics, Asia Publishing House.
6. Hogg R.V. and Tannis E.P. : Probability and Statistical Inference.
McMillan Publishing Co. Inc.
7. PitanJim : Probability, Narosa Publishing House. 8. Goon A.M., Gupta M.K., Dasgupta B. : Fundamentals of Statistics, Volume II :
The World Press Private Limited, Calcutta.
Course Code Title Credits
UAST 302 OPERATIONS RESEARCH AND INDUSTRIAL STATISTICS -1
2 Credits
(45 lectures )
Unit I : Linear Programming Problem (L.P.P.) :
Definition, Mathematical Formulation( Maximization and Minimization) Concepts of
Solution, Feasible Solution, Basic Feasible Solution, Optimal solution, Slack, Surplus & Artificial variable,
Standard form, Canonical form
Graphical Method & Simplex Algorithm to obtain the solution to an L.P.P. Problems
involving Unique Solution, Multiple Solution, Unbounded Solution and Infeasible Solution.
Big M method. Concept of Duality & its economic interpretation.
15 Lectures
Unit II : Transportation Problem
Definition, Mathematical Formulation Concepts of Feasible solution, Basic feasible solution, Optimal and multiple solutions.
Initial Basic Feasible Solution using
(i) North -West Corner rule.(ii) Matrix Minima Method.
(iii)Vogel’s Approximation Method. MODI Method for optimality.
Problems involving unique solution, multiple solutions, degeneracy, maximization,
prohibited route(s) and production costs. Unbalanced Transportation problem. 15 Lectures
Unit III : Assignment Problem and sequencing
Definition, Mathematical formulation. Solution by Hungarian Method.
Unbalanced Assignment problems.
Problems involving Maximization & prohibited assignments
Travelling salesman problem
Sequencing :
Processing n Jobs through 2 and 3 Machines and 2 jobs through m Machines.
15 Lectures
6
REFERENCES
1. Operations Research: Kantiswaroop and Manmohan Gupta. 4th Edition; S Chand & Sons.
2. Schaum Series book in O.R. Richard Broson. 2nd edition Tata Mcgraw Hill Publishing Company Ltd.
3. Operations Research: Methods and Problems: Maurice Sasieni, Arthur Yaspan and Lawrence Friedman,(1959), John Wiley & Sons.
4. Mathematical Models in Operations R esearch : J K Sharma, (1989), Tata McGraw Hill Publishing
Company Ltd.
5. Principles of Operations Research with Applications to Management Decisions: Harvey M. Wagner, 2nd Edition, Prentice Hall of India Ltd.
6. Operations Research: S.D.Sharma.11th edition, KedarNath Ram Nath& Company.
7. Operations Research: H. A.Taha.6th edition, Prentice Hall of India.
8. Quantitative Techniques For Managerial Decisions: J.K.Sharma , (2001), MacMillan India Ltd.
DISTRIBUTION OF TOPICS FOR PRACTICALS
SEMESTER -III
COURSE CODE UASTP3
Sr. No Semester III .Course
UASTP3(A) Sr. No Semester III .Course UASTP3(B)
1 Probability. 1 Formulation and Graphical Method
2 Discrete Random Variable 2 Simplex Method
3 Bivariate Probability
Distributions
3 Transportation
4 Binomial distribution 4 Assignment
5 Poisson distribution 5 Sequencing
6 Hyper geometric distribution
7
SEMESTER IV
Course Code Title Credits
UAST 401 STATISTICAL METHODS -2
2 Credits
(45 lectures )
Unit I : Continuous random variable:
Concept of Continuous random variable and properties of its probability distribution
Probability density function and cumulative distribution function.
Their graphical representation.
Expectation and variance of a random variable and its properties (with proof).
Meas ures of location, dispersion, skewness and kurtosis. Raw and central moments
(simple illustrations).
15 Lectures
Unit II : Some Standard Continuous Distributions :
Uniform, Exponential (location scale parameter ) , memory less property of Exponential distribution (without proof)
Cumulative distribution function,derivations of mean, median and variance for
Uniform and Exponential distributions. Properties of Normal distribution (without proof).
Normal approximation to Binomial and Poisson distribution (statement only).
Use of normal tables. 15 Lectures
Unit III : Elementary topics on Estimation and Testing of hypothesis:
Sample from a distribution : Concept of a statistic, estimate, sampling distribution, Parameter and its estimator.
Unbiasedness: Concept of bias and standard error of an estimator.
Central Limit theorem ( with proof ).
Sampling distribution of sample mean and sample proportion. (For large sample only)
Standard errors of sample mean and sample proportion. Point estimate and interval estimate of single mean, single proportion from sample of
large size.
Statistical tests :
Concept of hypothesis
Null and alternate hypothesis, Types of errors, Critical region, Level of significance.
Large sample tests (using central limit theorem, if necessary)
For testing specified value of population mean
For testing specified value in difference of two means
For testing specified value of population proportion For testing specified value of difference of population proporti on
(Development of critical region is not expected.)
Use of central limit theorem.
15 Lectures
8
REFERENCES:
1. Introduction to the theory of statistics: A M Mood, F.A. Graybill, D C Boyes; Third Edition;
McGraw -Hill Book Company.
2. Introduction to Mathematical Statistics: R.V.Hogg, A.T. Craig; Fourth Edition; Collier McMillan Publishers.
3. Probability and Statistical Inference: R.V.Hogg, E. A.Tannis, Third Edition; Collier McMillan Publishers.
4. John E. Freund’s Mathematical Statistics: I. Miller, M. Miller; Sixth Edition; Pearson Education Inc.
5. Introduction to Mathematical Statistics: P.G. Hoel; Fourth Edition; John Wiley & Sons Inc.
6. Fundamentals of Mathematical Statistics: S.C. Gupta, V.K. Kapoor; Eighth Edition; Sultan Chand & Sons.
7. Mathematical Statistics: J.N. Kapur, H.C. Saxena; Fifteenth Edition; S. Chand & Company Ltd.
8. Statistical Methods - An Introductory Text: J. Medhi; Second edition; Wiley Eastern Ltd.
9. An Outline of Statistical Theory Vol. 1: A.M. Goon, M.K. Gupta, B. DasGupta; Third Edition; The World Press Pvt. Ltd.
Course Code Title Credits
UAST 402 OPERATIONS RESEARCH AND INDUSTRIAL STATISTICS -2
2 Credits
(45 lectures )
Unit I : CPM and PERT
Concept of project as an organized effort with time management. Objective and Outline of the techniques.
Diagrammatic representation of activities in a project
Gantt Chart and Network Diagram.
Slack time and Float times. Determination of Critical path.
Probability consideration in project scheduling.
Project cost analysis. Updating.
15 Lectures
Unit II : GAME THEORY
Definitions of Two persons Zero Sum Game, Saddle Point, Value of the Game, Pure and Mixed strategy, Optimal solution of two person zero sum games. Dominance
property, Derivation of formulae for (2x2) game.
Graphical so lution of (2xn) and (mx2) games. Reduction of game theory to LPP
15 Lectures
Unit III : DECISION THEORY
Decision making under uncertainty: Laplace criterion, Maximax (Minimin) criterion, Maximin (Minimax) criterion, Hurwitz
criterion, Minimax Regret criterion.
Decision making under risk: Expected Monetary Value criterion, Expected
Opportunity Loss criterion, EPPI, EVPI.
Bayesian Decision rule for Posterior analysis.
Decision tree analysis along with Posterior probabilities. 15 Lectures
9
REFERENCES
1. Schaum Series book in O.R. Richard Broson. 2nd edition Tata Mcgraw Hill Publishing
Company Ltd.
2. Operations Research: Methods and Problems: Maurice Sasieni, Arthur Yaspan and Lawrence Friedman,(1959), John Wiley & Sons.
3. Mathematical Models in Operations Research : J K Sharma, (1989), Tata McGraw Hill Publishing Company Ltd.
4. Principles of Operations Research with Applications to Management Decisions: Harvey M. Wagner, 2nd Edition, Prentice Hall of India Ltd.
5. Operations Research: S.D.Sharma.11th edition, KedarNath Ram Nath& Compa ny.
6. Operations Research: H. A.Taha.6th edition, Prentice Hall of India.
7. PERT and CPM, Principles and Applications: Srinath. 2nd edition, East -west press Pvt. Ltd.
10 Kantiswarup, P.K. Gupta, Manmohan : Operations Research, Twelth edition, Sultan Chand & sons
11 Bronson R. : Theory and problems of Operations research, First edition, Schaum’s Outline series
12 Vora N. D. : Quantitative Techniques in Management, Third edition, McGraw Hill Companies. 13 Bannerjee B. : Operation Research Techniques for Management, First edition, Business Books
DISTRIBUTION OF TOPICS FOR PRACTICALS
SEMESTER -IV
COURSE CODE UASTP4
Sr. No Semester IV Course
UAST P4(A) Sr. No Semester IV Course UAST P4(B)
1 Continuous Random Variables 1 CPM - Drawing Network
2 Uniform, Exponential and
Normal Distributions 2 CPM - Determination of Critical Path and
related problems
3 Applications of central limit
theorem and normal
approximation
3 PERT
4 Testing of Hypothesis 4 Game Therory 1
5 Large Sample Tests 5 Game theory 2
6 Decision Theory -1: Decisions Under
Uncertainty
7 Decision Theory -2 : Decisions Under
Risk
8 Decision Theory -3 : Decision Tree
analysis.
10
Assessment of Practical Core Courses Per Semester per course
1. Semester work, Documentation, Journal .………. 10 Marks.
2. Semester E nd Practical Examination ----------- 40 Marks
Semester End Examination
Theory : At the end of the se mester, Theory examination of three hours duration and 100
marks based on the three units shall be held for each course.
Pattern of Theory question paper at the end of the semester for each course
:
There shall be F ive Questions of twenty marks each .
Question 1 based on all Three units . Ten sub- questions of two marks each.
Question 2 based on Unit I (Attempt any TWO out of THREE )
Question 3 based on Unit I I (Attempt any TWO out of THREE)
Question 4 based on Unit III (Attempt any TWO out of THREE)
Question 5 based on all Three Units combined. (Attempt any TWO out of THREE)
Practicals
: At the end of the semester, Practical examination of 2 hours duration and 40
marks shall be held for each course.
Marks for term work in each paper should be given out of 10.(5 for viva and 5 for journal)
Pattern of Practical question paper at the end of the semester for each course :
There shall be Four Questions of ten marks each. Students should attempt all questions.
Question 1 based on Unit I, Question 2 based on Unit II, Question 3 based on Unit III,
Question 4 based on all Three Units combined.
Students should attempt any two sub questions out of the three in each Question .
Workload
Theory : 3 lectures per week per course.
Practicals: 3 lecture periods per course per week per batch. All three lecture periods of the
practicals shall be conducted in succession together on a single day
*****************