FYBCom Mathematics Statistics_1 Syllabus Mumbai University by munotes
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SYLLABUS FOR MATHEMAT ICAL AND STAT ISTICAL TECHNIQUES AT
F.Y.B.Com. EXAMINATION
Revised Course
(WITH EFFECT FROM THE ACADEMIC YEAR 2016-2017)
Why Revision?
There is a Rapid expansion of knowledge in subject matter areas and improved instructional method
during last decade. There are considerable curricular revisions happening at the high school level.
Application of Mathematics and Statistics are widely used in industry and business. Keeping this in mind,
a revision of syllabus required in accordance with the growth of subject of at the high school level and
emerging needs of industry and its application.
Objective:
The main objective of this course is to introduce mathematics and statistics to undergraduate students
of commerce, so that they can use them in the field of commerce and industry to solve the real life
problems.
Distribution of topi cs and lectures
a.Workload :
Theory: 5 lectures per week of which 2 lectures are for Mathematics and 3 lectures for
Statistics.
Tutorial: 1 lecture per week per batch. Batch si ze is as prescribed by the University.
No. of working weeks in a semester: 15
Total no. of lectures in a semester : 15 * 5 = 75
b.Introductory lecture of about 120 minutes may be arranged for students who did not offer
general mathematics in the 9th & 10th Standard and/or Mathematics at the XIth and XIIth
to familiarize the students with the concept of Tabulation, Graphical Representation of
the data (basically Histogram and Ogives)
Semester I
Course
UBCOMFSI.6
Mathematical and Statistical Techniques-I Topic No. of lectures
Unit I 15
Unit II 15
Unit III 15
Unit IV 15
Unit V 15
Total 75
Total number of lectures 75 +Notional75 =150 lectures = 3 CREDITS
Semester II
Course
UBCOMFS
II.6
Mathematical Topic No. of lectures
Unit I 15
Unit II 15
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and
Statistical Techniques-II Unit III 15
Unit IV 15
Unit V 15
Total 75
Total number of lectures 75 +Notional 75=150 lectures = 3 CREDITS
MATHEMATICAL AND STATI
STICAL TECHNIQUES
WORKLOAD: MATHEMATICS : 2 lectures per week
STATISTICS : 3 lectures per week TUTORIAL : 1 per week
Tutorial batch size
: 25 Students
Semester I
Course: UBCOMFSI.6
Mathematical and Statistical Techniques-I
[A] MATHEMATICS: (40 marks)
Unit I: Shares and Mutual Funds
a. Shares: Concept of share, face value, market va lue, dividend, equity shares, preferential
shares, bonus shares. Simple examples.
b. Mutual Funds : Simple problems on calculation of Net income after considering entry
load, dividend, change in Net Asset Value (N .A.V.) and exit load. Averaging of price
under the Systematic Investment Plan (S.I.P.)
Unit II: Permutation, Combination and Linear Programming Problems:
a. Permutation and Combination: Factorial Notation, Fundamental principle of counting,
Permutation as arrangement, Simple exam ples, combination as selection, Simple
examples, Relation between rnCand rnP Examples on commercial application of
permutation and combination.
b. Linear Programming Problem: Sketching of graphs of (i) linear equation Ax + By + C
= 0 (ii) linear inequalities. Mathematical Formulation of Linear Programming Problems
upto 3 variables. Solution of Linear Program ming Problems using graphical method up to
two variables.
[B] STATISTICS: (60 marks)
Unit III: Su
mmarization Measures:
a. Measures of Central Tendencies: Definition of Average, Types of Averages: Arithmetic Mean,
Median, and Mode for grouped as well as ungrouped data. Quartiles, Deciles and Percentiles.
Using Ogive locate median and Quartiles. Using Histogram locate mode. Combined and
Weighted mean.
b. Measures of Dispersions: Concept and idea of dispersion. Various measures Range, Quartile
Deviation, Mean Deviatio
n, Standard Deviation, Variance, Combined Variance.
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Unit IV: Elementary P
robability Theory:
a.Probability Theory: Concept of random experiment/trial and possible outcomes; Sample
Space and Discrete Sample Space; Events th eir types, Algebra of Events, Mutually
Exclusive and Exhaustive Events, Complimentary events.
Classical definition of Probability, Add ition theorem (without proof), conditional
probability.
Independence of Events: P( A ∩ B ) = P(A) P(B). Simple examples.
b.Random Variable : Probability distribution of a disc rete random variable; Expectation
and Variance of random variable, simple exampl es on probability distributions.
Unit V: Decision Theory :
Decision making situation, Decision maker, Cour ses of Action, States of Nature, Pay-off and
Pay-off matrix; Decision maki ng under uncertain ty, Max imin, Max imax, Minimax regret and
Laplace criteria; simple examp les to find op timum d ecision. Formulatio n of Payoff Matrix.
Decision making under Risk, Expected Monetary Va lue (EMV) ; Decisi on Tree; Simple
Examples based on EMV. Expected Opportunity Loss (EOL), simple examples based on EOL.
Semest er II
Course: UBCOMFSII.6
Mathematical and Statist ical Techniques-II
[A] MATHEMATICS : (40 marks)
Unit I : Functions, Derivatives and Their Applications
a.Concept of real functions: constant function, linear function, xn , ex, ax, log x.
Demand, Supply, Total Revenue, Average Revenue, Total cost, Average cost and Profit
function. Equilibrium Point, Break-even point.
b.Derivative of functions:
i.Derivative as rate measure, Derivative of xn , ex, ax, log x.
ii.Rules of derivatives: Scal ar multiplication, sum, difference, product, quotient
(Statements only), Simple problem s. Second order derivatives.
iii.Applications: Marginal Cost, Marginal Re venue, Elasticity of Demand. Maxima and
Minima for functions in Economics and Commerce.
(Examination Questions on this unit s hould be application oriented only.)
Unit II: Interest and Annuity :
a.Interest: Simple Interest, Compound Interest (Nomin al & Effective Rate of Interest),.
Calculations involving upto 4 time periods.
b.Annuity: Annuity Immediate and its Present value, Future value. Equated Monthly
Installments (EMI) using reducing balance method & amortization of loans. Stated
Annual Rate & Affective Annual Rate Perpetu ity and its present value. Simple problems
involving up to 4 time periods.
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[B] STATISTICS: (60 marks)
Unit III: Bivariate Lin
ear Correlation and Regression
a.Correlation Analysis: Meaning, Types of Correlation, De termination of Correlation:
Scatter diagram
, Karl Pears on’s method of Correlation Coe fficient (excluding Bivariate
Frequency Distribution Table) and Sp earman’s Rank Correlation Coefficient.
b.Regression Analysis: Meaning, Concept of Regre ssion equations, Slope of the
Regression Line and its interpretation. Re gression Coefficients (excluding Bivariate
Frequency Distribution Table) , Relationship between Coe fficient of Correlation and
Regression Coefficients , Finding the equatio ns of Regression lines by method of Least
Squares.
Unit IV : Time series and Index Numbers
a.Time series : Concepts and components of a time series. Representation of trend by
Freehand Curve Method, Estimation of Tre nd using Moving Average Method and Least
Squares Method (Linear Trend only ). Estimation of Seasonal Component using Simple
Arithmetic Mean for Additive Model only (For Trend free data only). Concept of
Forecasting using Least Squares Method.
b.Index Numbers: Concept and usage of Index numb ers, Types of Index numbers,
Aggregate and Relative Index Numbers, Lasperye’s, Paasche’s, Dorbisch- Bowley’s,
Marshall-Edgeworth and Fisher’s ideal index numbers , Test of Consistency: Time
Reversal Test and Factor Reversal Test. Chain Base Index No s. Shifting of Base year.
Cost of Living Index Numbers, Concept of Real Income, Concept of Wholesale Price
Index Number. (Examples on missing values should not be taken)
Unit V: Elementary Probability Distributions
Probability Distributions:
i.Discrete Probability Distributi on: Binomial, Poisson (Properties and applications only, no
derivations are expected)
ii.Continuous Probability distribution: Normal Distribution. (Properties and applications
only, no derivations are expected)
Tutorial:
Two tutorials to be conducted on each unit i.e. 10 tutorials p er semester. At th e end of each
semester one Tutorial assignmen t of 10 marks should be given.
Exam ination:
Semester End Examination: 100 marks
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At the end of each semester, there will be a Semester End Examination of 100 marks , 3
hours duration and question paper patter n as shown below.
Question Paper Pattern :( Course: UBCOMFSI.6 and Course: UBCOMFSII.6)
1. In Section I (based on Mathematics), Two questions carrying 20 marks each. First
question should be on Unit I and Second question should be from Unit II .
2. In each question there should be five sub-questions carrying 5 marks each. Students
should be asked to answer any 4 sub questions from each question.
3. In Section II (based on Statistics), Three questions carrying 20 marks each. First
question should be on Unit III, Seco nd question should be from Unit IV and third
question should be from Unit V.
4. In each question there should be five sub-questions carrying 5 marks each. Students
should be asked to answer any 4 sub questions from each question.
Reference Books:
1. Mathematics for Economics and Finance Methods and Modelling by Martin Anthony and
Norman Biggs, Cambridge University Press, Cambridge low‐priced edition, 2000, Chapters 1, 2,
4, 6 to 9 & 10.
2. Applied Calculus: By Stephen Waner and Steven Constenoble, Brooks/Cole Thomson Learning,
second edition, Chapter 1 to 5.
3. Business Mathematics By D. C. Sancheti and V. K. Kapoor, Sultan Chand & Sons, 2006, Chapter 1,
5, 7, 9 &10.
4. Mathematics for Business Economics: By J. D. Gupta, P. K. Gupta and Man Mohan, Tata Mc‐
Graw Hill Publishing Co. Ltd., 1987, Chapters 9 to 11 & 16.
5. Quantitative Methods‐Part‐I By S. Saha and S. Mukerji, New Central Book Agency, 1996,
Chapters 7 & 12.
6. Mathematical Basis of Life Insurance By S.P. Dixit, C.S. Modi and R.V. Joshi, Insurance Institute of
India, Chapters 2: units 2.6, 2.9, 2.20 & 2.21.
7. Securities Laws & Regulation of Financial Market : Intermediate Course Paper 8, Institute of
Company Secretaries of India, Chapter 11.
8. Investments By J.C. Francis & R.W. Taylor, Schaum’s Outlines, Tata Mc‐Graw Hill Edition 2000,
Chapters 2,4 & section 25.1.
9. Indian Mutual Funds Handbook : By Sundar Shankaran, Vision Books, 2006, Sections 1.7,1.8.1,
6.5 & Annexures 1.1to 1.3.
10. STATISTICS by Schaum Series.
11. Operations Research by Gupta and Kapoor
12. Operations Research by Schaum Series
13. Fundamentals of Statistics ‐ D. N. Elhance.
14. Statistical Methods ‐ S.G. Gupta (S. Chand & Co.
15. Statistics for Management ‐ Lovin R. Rubin D.S. (Prentice Hall of India)
16. Statistics ‐ Theory, Method & Applications D.S.Sancheti & V. K. Kapoor.
17. Modern Business Statistics ‐ (Revised} ‐B. Pearles & C. Sullivan –Prentice Hall of India.
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18. Business Mathematics & Statistics : B Aggarwal, Ane Book Pvt. Limited
19. Business Mathematics : D C Sancheti & V K Kapoor, Sultan Chand & Sons
20. Business Mathematics : A P Verma, Asian Books Pvt. :Limited.
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QUESTION PAPER – SET I
MARKS: - 100 TIME: - 3 HRS
N.B : (1) ALL QUESTION ARE COMPALSORY
(2) ALL QUESTION CARRY EQUAL MARKS
(3) FIGURES TO THE RIGHT INDICATES MARKS TO A SUB -QUESTION.
(4)GRAPGH PAPER WILL BE SUPPLIED ON REQUEST.
(5)USE OF NON -PROGRAMMABLE CALCULATOR IS ALLOWED.
SECTION- I
Q.1 ATTEMPT ANY FOUR OF THE FOLLOWING
(a) 5 Marks (b) 5 Marks (c) 5 Marks (d) 5 Marks (e) 5 Marks 20 Marks
Q.2 ATTEMPT ANY FOUR OF THE FOLLOWING
(a) 5 Marks (b) 5 Marks (c) 5 Marks (d) 5 Marks (e) 5 Marks 20 Marks
SECTION- II
Q.3 ATTEMPT ANY FOUR OF THE FOLLOWING
(a) 5 Marks (b) 5 Marks (c) 5 Marks (d) 5 Marks (e) 5 Marks 20 Marks
Q.4 ATTEMPT ANY FOUR OF THE FOLLOWING
(a) 5 Marks (b) 5 Marks (c) 5 Marks (d) 5 Marks (e) 5 Mar ks 20 Marks
Q.5 ATTEMPT ANY FOUR OF THE FOLLOWING
(a) 5 Marks (b) 5 Marks (c) 5 Marks (d) 5 Marks (e) 5 Marks 20 Marks