SYLLABUS & PROGRAMME STRUCTURE

Statistics (Honours)

(Choice Based Credit System)

(Effective from the Academic Session 2017-2018)

First Semester

MAHARAJA BIR BIKRAM UNIVERSITY AGARTALA, TRIPURA: 799004

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PROGRAMME STRUCTURE

Structure of Proposed CBCS Syllabus BA/BSc/BCom Honours

Semester Core Course

(14)

Honours

Ability

Enhancement

Compulsory Course

(AECC) (2)

Skill

Enhancement

Course (SEC)

(2)

Discipline

Specific

Elective

(DSE) (4)

Generic Elective

(GE) (4)

1 C1

C2

AECC1:

Environmental

Science

GE1

(Paper-I of selected

subject other than

Hons subject)

2 C3

C4

AECC2 :

(English/MIL

(Communication)

GE2

(Paper-II of

selected subject

other than Hons

subject)

3 C5

C6

C7

SEC1 GE3

(Paper-III of

selected subject

other than Hons

subject)

4 C8

C9

C10

SEC2 GE4

(Paper-IV of

selected subject

other than Hons

subject)

5 C11

C12

DSE1

DSE2

6 C13

C14

DSE3

DSE4

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First Semester

Core Course - Paper- I

Descriptive Statistics & Basic Concepts of Probability

TOTAL MARKS – 100

(Theory – 70, Practical-30)

Unit I (Statistical Methods)

Introduction to Statistics: Definition, scope and Limitations of statistics, Use of statistics.

Collection and classification of data: Primary data and secondary data, methods of collection

of data, Scrutiny of data. Classification, principles of classification, types of classification.

Tabular presentations of data. Diagrammatic representation of data. Frequency

distribution and its constructions. Graphical presentations of frequency distribution.

Unit II (Central tendency, Dispersion & Moments)

Concept of central tendency, Different measures of central tendencies. Empirical

relationships between different measures. Concept of dispersion, Different measures of

dispersion and their properties. Different types of moments, relationships between raw and

central moments. Sheppard's corrections for moments (without proof). Skewness and

Kurtosis and their measures. Boxplot.

Unit III (Bivariate Correlation & Regression)

Bivariate data, Scatter diagram, Correlation coefficient and its properties. Rank correlation-

Spearman's & Kendall's measures.

Principle of Least squares. Concept of regressions, Regression lines, Important results

relating to regression lines. Fitting of Polynomial, Inverse, Exponential and Growth curve.

Unit IV (Probability)

Random experiment, Sample point, Sample space, different types of Events, Meaning of

Probability, Classical, Statistical and Axiomatic definitions of Probability. Limitation of

classical definition of Probability, Theorem on the Probability of union of Events.

Conditional Probability, Theorem on conditional Probability, Statistical independence of

Events, Bayes' theorem and its application.

Practical

List of Practical (Computational tools: Electronic Calculator & Spreadsheet Softwares)

1. Graphical representation of non-frequency data (Bar-Diagram, Line-Diagram, Pie

chart, Stem-and-leaf plot, Pictograms).

2. Construction of frequency distribution (Grouped & Ungrouped).

3. Graphical representation of frequency data (Histogram, Frequency polygon, Ogives,

Boxplots).

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4. Summary statistics (Raw, Grouped & Ungrouped data).

5. Pearson’s correlation coefficient & Linear regression.

6. Spearman's rank correlation coefficient.

7. Kendall's correlation coefficient.

8. Curve fitting by least square method: Linear, Polynomial, Inverse, Exponential and

Growth curve.

9. Random Experiments & Computation of Probabilities for different Events.

Suggested Reading

1. Goon A.M., Gupta M.K. & Dasgupta B. (2002): Fundamentals of Statistics (Vol-I),

World Press, Kolkata.

2. Goon A.M., Gupta M.K. & Dasgupta B. (1994): An Outline of Statistical Theory

(Vol-I), World Press, Kolkata.

3. Rohatgi V.K. (1984): An Introduction to Probability Theory & Mathematical

Statistics, John Wiley.

4. Kendall M.G. & Stuart A. (1966): Advanced Theory of Statistics (Vol-I & II).

5. Gupta S. C., Kapoor V. K.: Fundamentals of Mathematical Statistics, Sultan Chand &

Sons.

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First Semester

Core Course - Paper- II

Essential Mathematics for Statistics

TOTAL MARKS – 100

(Theory – 70, Practical-30)

Unit I (Elementary Mathematics)

Permutation & combination, Arithmetic & Geometric Progression. Binomial expansion for

positive & negative indices. Series Expansions of Exponential and Logarithmic Functions.

The principle of mathematical induction.

Unit II (Calculus & Mathematical Analysis)

Limit, Continuity and Differentiability of functions. Total & Partial Differentiation.

Maximum and Minimum of univariate & bivariate functions. Integration of univariate &

bivariate functions. Beta & Gamma Integration.

Convergence of sequence and series, Absolute convergence, Simple tests of

convergence (root test and ratio test), Basic concepts of Pointwise convergence and Uniform

convergence.

Unit III (Vector & Matrix Algebra)

Basic concept on Vector space with real field, Linear dependence of vector, Basis and

dimension of a vector space., Orthogonal vectors.

Definition of a Matrix, Different types of matrix, Matrix operations, Elementary

matrices and their uses, Rank of a matrix, Inverse of a matrix, Determinants, Quadratic

forms, Reduction of Quadratic form to canonical form. Basic concept of Characteristic roots

and vectors.

Unit IV (Numerical Analysis)

Interpolation: Difference operators (, E, D), Polynomial approximation, Difference table,

Newton's forward and backward interpolation formulae, Lagrange's interpolation formula.

Numerical Integration: Trapezoidal & Simpson's one-third rules. Euler maclaurin

summation formula.

Numerical solutions of univariate equation: Bisection, Iteration & Newton-Raphson

methods. Convergences of Iteration and Newton-Raphson methods.

Stirling’s approximation to n! for large n.

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Practical

List of Practical (Computational tools: Electronic Calculator & Spreadsheet Softwares)

1. Interpolation by Newton's forward, Newton's backward & Lagrange's interpolation

formulae.

2. Numerical Integration by Trapezoidal & Simpson's one-third rules.

3. Numerical solutions of univariate equations by Bisection, Iteration & Newton-

Raphson methods.

4. Determinant of Matrix by Pivotal condensation method.

5. Inversion of Matrix by Gauss-Jordan method.

6. Solution of linear equations by Gauss elimination & Gauss Jordan methods.

7. Computation of Characteristic roots and vectors.

Suggested Reading

1. Kalyan K. Mukherjee: Numerical Analysis, New Central Book Agency (P) Ltd,

Kolkata.

2. Goon A.M., Gupta M.K. & Dasgupta B. (1994): An Outline of Statistical Theory

(Vol-I), World Press, Kolkata.

3. Sastry S.S(1987): Introductory Methods of Numerical Analysis, Prentice Hall..

4. Jain, Iyengar, Jain: Numerical Methods, New Age International Publishers.

5. J.B. Scarborough: Numerical Mathematical Analysis, Oxford and IBH.

6. S. C. Malik, Savita Arora: Mathematical Analysis, New Age International Publishers.

7. A. M. Goon: Vectors & Matrices, World Press, Kolkata.