Honours Second Year Syllabus & Book List Department of Statistics

 NATIONAL UNIVERSITY

Honours Second Year Syllabus Department of Statistics

 

Discrete Distributions: Detail study of Bernoulli, Binomial, Poisson, Negative Binomial, Geometric, Hyper geometric, Uniform distributions and their properties. Multinomial distribution.

Continuous Distributions: Detailed study of Normal, Exponential, Uniform, Beta, Gamma, Cauchy, Weiball, Laplace, Maxwell distribution.

Bivariate Distribution: Detailed study of Bivariate normal, Bivariate bionomial, Bivariate poisson distribution & Bivariate beta.

Books Recommended

 

1	Roy, M.K	Fundamentals of Probability & Probability Distribution
2	Mardia, K.V.	Families of Bivariate Distribution, Charles Griffen & Co
3	Islam, M.N.	An Introduction to Statistics and Probability, Mullick and Brothers
4	Johnson	Univariate Continuous Distribution Part I & II, Wiley Publication
5	Bhuiyan , K C	Probability distribution and Statistical Inference.

 

Introduction: Basic concept of sample survey, relative advantages, disadvantages and suitability of complete and sample enumeration. Uses of sample survey. Role of sampling theory. Requirements of a good sample design.

 

বিষয়সমূহঃ

• 223601 - Probability Distribution (100)
• 223603 - Sampling Technique (100)
• 223605 - Linear Algebra (100)
• 223707 - Calculus II (100)
• 222211 - Money, Banking and Public finance (100)
• 222213 - Bangladesh Economy (50)
• 221109 - English (Compulsory) (100-Non credit)
• 223606 - Lab-3: Probability Distribution and Sampling Technique (50)
• 223608 - Lab-4: Linear algebra (50)
• 223708 - Math Lab (50)

Preliminaries in Sample Survey : Units, Population, Sampling units, Sampling frame. Basic principles of sample survey. Various steps involved in a sample survey. Pilot survey, Random or probability sampling and Non-random or purposive sampling. Quota sample. Mixed sample. Convenience sampling snowball sampling.

 

Population Values and Estimates in Sample Survey: Bias and its effect. Precision and accuracy of estimates. Different type of errors associated with sampling such as sampling error  & non sampling errors and complete enumeration. Various methods of data collection. Questionnaire and schedule. Preparation of questionnaire. Open and closed questionnaire. Different types of random sampling.

 

Simple Random Sampling: Advantages and disadvantages, Drawing of samples with and without replacement sampling, estimates and standard errors. Simple random sampling for

proportion-estimate and standard errors. Determination of sample size for specified precision. Introduction to other probability sampling schemes.

Stratified Random Sampling: Reasons for stratification. Formation and number of strata. Stratified random sampling, estimator, standard error. Allocation of samples to strata.

 

  Cluster Sampling: Reasons for clustering, formation of clusters, size of clusters. Simple cluster sampling with equal size clusters-estimates and standard error, comparison with simple random sampling. Two stage sampling.

Systematic Sampling : Use, limitation, estimates, bias, standard error and efficiency. Comparisons with simple random sampling. Systematic sampling for populations with linear trend. Methods for dealing with population with linear trend or periodic variation.

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Books Recommended:

 

1	Cochran, W.G.	Sampling Technique
2	Islam, M.N.	An Introduction to Sampling Methods (3rd Edn), Mullick & Brothers
3	Kish, L.	Survey Sampling
4	Hansen,       Hurwitz      and Madow	Sample Survey: Methods and Theory, Vol-1 & Vol-2
5	Sukhatme, P.V.	Sampling Theory of Surveys with Application
6	Daroga Singh	Sampling Technique

 

Vector Set: Length angle between two vectors of normalized vectors, Unit vector sets, linearly dependent and independent vectors Orthogonal vectors, Gram- Schmidt orthogonalization process, Normalization & sweep-out process, vector space & Sub-space and their rank & basis, sub-set & Superset of vectors and related theorems.

 

Determinant and Matrix: Distinction between square matrix and determinant. Evaluation of n×n determinants & their properties and uses in statistics. Different types of matrices; definitions with examples, matrix operations, rank and elementary transformation of matrices, related theorems of ranks, trace of a matrix, its properties with proofs.

 

Usual inverse of matrices and their uses in statistics. Generalized inverses & Kronecker product of matrices and their properties and uses. System of linear equations: homogeneous and nonhomegeneous types of linear equations, consistent and inconsistent, unique solutions, solution of such equations. Quadratic forms, Canonical forms, Latent roots & vectors and their related theorems and uses in statistics, orthogonal matrices, Idempotent matrices, patterned

matrices etc and their properties. Vector & matrix differentiations and their application in statistics.

 

Books Recommended:

1	Santirarayan.	A Textbook of Matrices.
2	Agarwal, D.	Advanced Integral Calculus
3	Scrale, S.R	Linear Models
4	Rao, C.R. & Mitra	Generalized Inverses and its Application
5	Ali, M. I	Matrix Algebra
6	Abdur Rahman	College Linear Algebra

  

Probability Distributions: Fitting of Binomial, Poisson and Normal distribution.

Sample Survey: Drawing of sample by SRS, Stratified sampling, systematic sampling, cluster sampling with equal size. Estimation of parameters in each case. Estimation of variance of the estimates of the parameters, determination of precision of estimates. Relative efficiency of different sampling scheme.

  

Vector: Rank basis, dimension & orthogonal vectors by the Gram- Schmidt orthogonalization process, orthonormal vectors, linear dependence and independence of vectors etc.

 

Linear Algebra: Rank of a matrix, transpose, Determinant inversion, Trace, Solutions of simultaneous equations, quadratic form. Latent roots and latent vectors of the matrix.

 

 

1.      Vector valued functions of a single variable: Limits. Derivatives and integrals. Tangent lines to graphs of such functions. Arc length from vector viewpoint. Arc length parameterization.

 

2.      Curvature of space curves: Definition. Curves of zero curvature. Curves of constant non-zero curvature.Cartesian equations and parametric equations. Radius of curvature. Centre of curvature.

3.      Functions of several variables: Limits and continuity. Partial derivatives. Differentiability, linearization and differentials. The chain rule. Partial derivatives with constrained variables. Directional derivatives, gradient vectors and tangent planes.

Extreme values and saddle points of functions of several variables. Lagrange multipliers. Taylor’s formula.

 

4.      Multiple Integration: Double integrals and iterated integrals. Double integrals over nonrectangular regions. Double integrals in polar coordinates. Area by double integrals. Triple integrals and iterated integrals. Volume as a triple integral. Triple integral in cylindrical and spherical coordinates. General multiple integrals. Jacobians.

 

5.      Topics in Vector Calculus: Scalar and vector fields, Gradient, divergence and curl, and their properties. Line integrals, Independence of paths. Green’s theorem. Surface integrals. Stokes’ theorem. The divergence theorem.

 

Books Recommended: Howard Anton-Calculus 5/E (and forward edition)

 

Getting started. Problem solving using Mathematical /Maple (Problems will be selected from Papers studied in the first and second years of their studies).

Students are required to work on their assignments in MMT 201 in the lab sessions.

 

  

Money: Definition, functions, importance, types of money.

 

Value of money: Meaning, quantity theory of money, cash transaction and cash balance approach, concept of inflation and deflation.

 

Commercial Banking: Functions, Balance sheet, liquidity and profitability. Multiple credit creation of commercial banks. Commercial Banks of Bangladesh.

 

Central Banking: Objective, Functions, Credit Control of central bank. Bangladesh Bank.

 

Specialized Banking: Objective, Importance. Role of BSB, BSRS, BKB, Islami Bank, Grameen Bank.

 

Public Finance: Definition, Nature and Scope, Distinction between public finance and private finance, Role of public finance in developing countries.

 

Public Revenue: Sources, tax & fees, impact & incidence of taxes, direct & indirect taxes, value added tax.

 

Public Expenditure: Need for public expenditure & its increasing importance.

 

Budget: Concept of budget. Distinction between revenue and capital budget, public debt. Sectoral allocation. Study of the budgets of Bangladesh (last five years).

 

Characteristics of the Economy of Bangladesh: Obstacles & preconditions of economic development. Agricultural resources, its importance and problems.

 

Population in Bangladesh: Its growth, structure & distribution Problem, family planning, unemployment problem.

 

Industry in Bangladesh: Importance of industrialization, structure of industry. Problems & prospect of industries.

 

Books Recommended:

 

1	Crowther	Outline of Money
2	Luckett	Money & Banking
3	Musgrave	Theory of Public Finance
4	Due	Government Finance.
5	Faaland & Parkinson	Bangladesh : A Test case of Development
6	A. R. Khan	Strategy of Development in Bangladesh Macmillan, 1989

  

Characteristics of Bangladesh Economy: Natural resource. obstacles & precondition of economic development.

National Income: Sectoral contribution. Importance of agriculture, its problems, cropping pattern. HYV technologies, institutional reforms.

Industrialization: Importance of industrialization. sericulture of industry, problems and prospects of small scale industry.

Population: Growth, structure & distribution problem, family planning, unemployment problem.

Foreign trade of Bangladesh: Characteristics role, international co-operation.

A Study of the Budgets of Bangladesh (last five years): State of the revenue budget, state of the capital (development) budget, sources of funding of development expenditure.  Relative importance of direct and indirect taxes.

Planning in Bangladesh: Objectives, problems, development plans in Bangladesh.

 

Aims and objectives of this Paper:

To develop students’ English language skills, to enable them to benefit personally and professionally. The four  skills                listening, speaking, reading and writing will be integrated to encourage better language use.

1.       Reading and understanding                                                                                                                    5 4=20

 

Students will be expected to read passages that they might come across in their everyday life, such as newspapers, magazines, general books etc. Simple stories will also be included to give students a familiarity with different uses of the language.

 

 

[N.B. : 5 Questions are to be answered. Each question will carry 4 marks. There may be division in each question]

a)    Understanding different purposes and types of readings
b) Guessing word-meaning in context.
c)     Understanding long sentences
d) Recognizing main ideas and supporting ideas.
e)     Answering comprehension questions.
f)     Writing summaries.
2.    Writing a)       Writing correct sentences, completing sentences and combining sentences.	5	40
b) Situational writing : Posters, notices, slogans, memos, advertisements etc.	4

c)       Paragraph writing : Structure of a paragraph; topic sentences; developing ideas; writing a conclusion; types of paragraphs (narrative, descriptive, expository, persuasive); techniques of paragraph development (such as listing, cause and effect, comparison and contrast).                                                                   8

Or,

d)       Newspaper writing : Reports, press releases dialogues etc.

e)       Writing resumes.                                                       Or,                                                                    8

f)        Writing letters : Formal and informal letters, letters to the editor, request letters, job applications, complaint letters etc.

g)       Essay : Generating ideas; outlining; writing a thesis sentence; writing the essay: writing introductions, developing ideas, writing conclusions; revising and editing.                                       15

3.   Grammar                                                                                                                                                     25

a)         Word order of sentences.

b)       Framing questions.

c)       Tenses, articles, subject-verb agreement, noun-pronoun agreement, verbs, phrasal verbs, conditionals, prepositions and prepositional phrases, infinitives, participles, gerunds. (Knowledge of grammar will be tested through contextualised passages).

d)       Punctuation.

4.       Developing vocabulary : Using the dictionary, suffixes, prefixes, synonyms, antonyms, changing word forms (from verb to noun etc.) and using them in sentences.                                                                                     10

5.       Translation from Bengali to English.                                                                                         1 5=5

6.       Speaking skills : Speaking skills should be integrated with writing and reading in classroom activities.

The English sound system; pronunciation skills; the IPA system; problem sounds, vowels, consonants and dipthongs; lexical and syntactic stress.

(Writing dialogue and practising it orally students can develop their speaking skill. Dialogue writing can be an item in writing test.)