1
SOLAPUR UNIVERSITY, SOLAPUR.
SYLLABUS
FOR
B.Com. Part-III (Semester Pattern)
IN
ADVANCED STATISTICS
To be effective from the academic year 2012-13 (June-2012).
2
Solapur University, Solapur
Semester Pattern Syllabus
B.Com.III (Semester-V)
(Optional)
ADVANCED STATISTICS (Paper–I)
(W.e.f. June 2012)
Unit–I: Graphical and Diagrammatic Representation of Data
Deviation Bars, Subdivided Multiple Bars, Squares, Cubes.
Pie Diagram, Angular Diagram, Pictogram, Range Graph, Band Graphs.
Examples.
(15)
Unit–II: Permutations and Combinations
Definitions and Relations between them,
Permutations and Combinations in a Circle.
Binomial Theorem (without proof)
Simple example.
(12)
Unit–III: Probability Theory
Definition of terms used in probability, Definition of probability,
Definition of conditional probability
Additive & Multiplicative theorems on probability,
Bays theorem, Examples based on these
(15)
Unit- IV: Random Variable and Probability Distribution
Meaning of random variable.
Concept of discrete & continuous random variables.
Definition of Probability mass function & Probability density function,
Distribution function. Definition of Bivariate discrete randomvariable.
Joint probability mass function of X & Y,
Marginal & Conditional Probability Distributions.
(15)
Reference Books:
1) A Text Book of Calculus – Bhagwat & Pawate
2) Statistical Methods by S.P.Gupta.
3) Mathematical Statistics by Saxena & Kapoor.
4) Statistics by Sancheti & Kapoor.
5) Introduction to Mathematical Statistics by D.N.Elance.
6) Exercises in Probability, by T. Cacoullous, Narosa Publishing house Delhi
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Solapur University, Solapur
Semester Pattern Syllabus
B.Com.III (Semester-VI)
(Optional)
ADVANCED STATISTICS (Paper – I)
(W.e.f. June 2012)
Unit-I: Mathematical Expectation
Definition of Mathematical Expectation of Univariate & Bivariate discrete
random variable X. Addition & multiplication laws of mathematical
expectation for discrete random variable only.
Examples based on these. Mean & Variance of discrete random variable.
Conditional mean & Conditional Variance. Examples.
(18)
Unit-II: Binomial Distribution
Definition of p.m.f., Mean & Variance of Binomial Distribution . Properties
of Binomial Distribution. Condition under which binomial distribution is
applicable. Examples.
(15)
Unit-III: Poisson Distribution
Definition of p.m.f., Mean & Variance of Poisson Distribution. Properties
of Poisson Distribution. Condition under which Poisson distribution is
applicable. Examples.
(15)
Unit-IV: Normal Distribution
p.d.f. of Normal Distribution, S.N.V., Normal Probability curve. Properties
of normal distribution. Examples based on area under normal curve.
(15)
Reference Books:
1) Fundamentals of Statistics, by S.C.Gupta, Himalaya Publication
2) Statistical Methods by S.P.Gupta.
3) Mathematical Statistics by Saxena & Kapoor.
4) Statistics by Sancheti & Kapoor.
5) Introduction to Mathematical Statistics by D.N.Elance.
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Solapur University, Solapur
Semester Pattern Syllabus
B.Com.III (Semester-V)
(Optional)
ADVANCED STATISTICS (Paper – II)
(W.e.f. June 2012)
Unit-I: Demography
Introduction, Measures of Mortality (CDR, SDR, STDR by Direct Method)
Measures of fertility (CBR, GFR, SFR, TFR)
Reproduction rates: Crude rate of Natural Increase.,GRR & NRR.
(15)
Unit-II: Testing of Hypotheses
Definition of parameter, statistic, hypothesis (Simple & Composite) Null &
alternative hypothesis, critical region, level of significance, Type I & Type
II errors, power of the test (Only concepts)
(12)
Unit-III: Large Sample Tests
1) Test for an assumed mean.
2) Test for an assumed Proportion.
3) Comparison of means of two populations.
4) Comparison of proportion of two populations.
(15)
Unit-IV: Exact Sampling Distributions
Definition of Chi-square, t and F variates and their p.d.fs.
Applications of t distribution:
1) Testing H 0 : M = M 0 2) Testing H 0 : M1 = M 2
(18)
Applications of Chi-square distribution:
1) Test of goodness of fit
2) Testing independence of attributes. 2 × 2 contingency table.
Applications of F – distribution: 1) To test H 0 : σ12 = σ 22
Reference books:
1) Fundamentals of applied statistics by Gupta & Kapoor.
2) Statistical Methods by J.Medhi
3) Fundamentals Mathe. Statistics by Gupta & Kapoor.
4) Introduction to Mathe. Statistics by D.N.Elance.
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Solapur University, Solapur
Semester Pattern Syllabus
B.Com.III (Semester-VI)
(Optional)
ADVANCED STATISTICS (Paper – IV)
(W.e.f. June 2012)
Unit-I: Linear Programming Problems
Introduction, concept, Mathematical formulation of the Problem. Solution
by using graphs problems & Examples based on l.p.p.
(15)
Unit-II: Assignment Problems
Assignment Problems for minimization, introduction, Mathematical
formulation Hungarian algorithm, problems on A.P.
(15)
Unit-III: Transportation Problems
Transportation Problems for minimization, introduction, methods of finding
I.B.F.S., testing solution for optimality, , problems on T.P.
(15)
Unit-IV: Sequencing
Introduction, Assumptions, problem of sequencing of n jobs through 2
machines, n jobs through 3 machines, n jobs through M machines, actual
problems on this.
(15)
Reference books
1) A text book of operations research by S.D. Sharma
2) Quantitative techniques in decision making by J.K. Sharma
3) A text book of operations research by R.K. Gupta.
4) Quantitative Techniques by Taha
5) Quantitative Techniques by C. Kothari
*****
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Solapur University, Solapur
Nature of Question Paper For Semester Pattern
• Faculty of Commerce (B.Com., M.Com.)
Model Question Paper
(w.e.f. June 2012)
Time: - 2 hrs.
Q. 1
Q. 2
Q. 3
Multiple choice questions
(four alternatives should be given)
1 ---------------------------------------------------(a)
(b)
(c)
(d)
2
3
4
5
6
7
8
9
10
Answer the following
(Short note/Short problem/Short answer)
(A)
(B)
Answer the following
(Short note/Short answer/Short problem)
(A)
(B)
Total Marks-50
10
05
05
05
05
Q. 4
Answer any one (Long answer/Problem)
i)
ii)
10
Q. 5
Answer any one (Long answer/Problem)
i)
ii)
10