Download Paper-101 : Probability Theory

SYLLABUS
B.A./B.Sc. (Statistics) Part – I
For Examination of Session 2010, 2011 & 2012
Paper-1 : Probability Theory
Max. Marks : 100
Pass Marks : 35%
Total Lectures : 120 Periods (of 45 minutes each)
to be delivered
Time Allowed
: 3 hours
INSTRUCTIONS FOR THE PAPER SETTER
The question paper will consist of five sections : A, B, C, D and E. Sections A, B, C and D
will have two questions from the respective sections of the syllabus and will carry 20 marks each
.Section E will consist of one question having 8/10 objective/very short-answer type questions
covering the entire syllabus uniformly .All the questions from the sections A ,B ,C ,D and E will carry
equal marks.
INSTRUCTIONS FOR THE CANDIDATES
Candidates are required to attempt one question each from the sections A, B, C and D of the
question paper and the entire section E. All questions will carry equal marks.
SECTION-A
Important concepts in probability :Random experiment, trial, sample point and sample space,
definition of an event, mutually exclusive, exhaustive, independent and equally likely events.
Definition of the probability-classical and relative frequency approach to probability, their demerits and
axiomatic approach to probability. Properties of probability based on axiomatic approach, conditional
probability, Bayes theorem and its applications.
SECTION- B
Random Variable : Definition of random variables, probability mass function, continuous random
variable, probability density function illustrations of random variables and its properties, expectation of
a random variable and its properties-moments, measures of location and dispersion, moment generating
function and probability generating function. Two dimensional random variables –joint, marginal and
conditional distributions .
SECTION-C
Standard univariate discrete distributions and properties : Uniform, Binominal, Poisson, Hyper
Geometric, Geometric and Negative Binomial distributions. Continuous univariate distributions :
Uniform , normal , exponential, Gamma, Beta and chi-square distributions.
SECTION-D
The bivariate mormal distribution, the marginal and conditional probability distributions associated
with the bivariate normal distribution (without derivation).
Chebyshev's inequality and its applications, statements and applications of weak law of large numbers
and central limit theorems (De-moivre's-Laplace and Lindeberg-Levy versions).
1.
2.
3.
1.
2.
TEXT BOOKS
P.L. Meyer ( 1970 ) : Introductory Probability and Statistical Applications Addison-Wesley.
Goon, A.M., Gupta, M.K., Dasgupta, B.(1999) : Fundamental of Statistics, Vol. I, World
Press ,Calcutta .
Mood A.M., Graybill F.A and Boes D.C. (1974) : Introduction to the Theory of Statistics,
McGrawh Hill .
REFERENCE BOOKS
Bhat B.R, Srivenkatramana T and Rao Madhava K.S. (1997) : Statistics : A Beginner's Text,
Vol. II, New Age International (P) Ltd.
David S (1996) : Elementary Probability, Oxford Press.John E. Freund's Mathematical
Statistics 6th Ed. Pub. Pearson Education.
Paper-II : Descriptive Statistics
Max. Marks : 100
Pass Marks : 35%
Total Lectures : 120 Periods (of 45 minutes each)
to be delivered
Time Allowed
: 3 hours
INSTRUCTIONS FOR THE PAPER SETTER
The question paper will consist of five sections : A, B, C, D and E. Sections A, B, C and D
will have two questions from the respective sections of the syllabus and will carry 20 marks each
.Section E will consist of one question having 8/10 objective/very short-answer type questions
covering the entire syllabus uniformly .All the questions from the sections A ,B ,C ,D and E will carry
equal marks.
INSTRUCTIONS FOR THE CANDIDATES
Candidates are required to attempt one question each from the sections A, B, C and D of the
question paper and the entire section E. All questions will carry equal marks.
SECTION- A
Collection of data : Primary data – designing a questionnaire and a schedule. Secondary data - its
major sources including some government publications.Concept of a Statistical population and samples
from a population ;quantitative and qualitative data , discrete and continuous data, nominal, ordinal ,
ratio & interval scales .
Presentation of data: Diagrammatical representation of data , frequency distribution ,
graphical representation , Histogram , Frequency polygon , Frequency curves and ogives .
SECTION-B
Analysis of quantitative data : univariate data concepts of central tendency , dispersion , skewness and
kurtosis and their measures including those based on quartiles and moments, Sheppard's correction
for moments (without derivation).
SECTION-C
Bivariate data :scatter diagram, product moment correlation coefficient, properties and coefficient of
determination. Spearman's rank correlation coefficient . Concept of errors in regression, principle of
least square, fitting of linear regression and related results.
SECTION-D
Multivariate data : multiple and partial correlation in three variables (only results no derivations).
Analysis of categorical data : Contingency of categorical data ,independence & association
of attributes . Various measures of association for two way classified data.
1.
Goon, A.M., Gupta
M.K., Dasgupta, B.
2.
3.
4.
5.
6.
TEXT BOOKS
Fundamental of Statistics. Vol. 1. 1991, world
Press. Calcutta.
RECOMMENDED READINGS
Bhat B.R, Srivenkatramana T and Rao Madhava K.S. (1997): Statistics : A
Beginner's Text, Vol, I , New Age International (P) Ltd.
Croxton F.E, Cowden D. J and Kelin S (1973) : Applied General statistics, Prentice Hall
of India .
Spiegel, M.R. (1967): Theory & Problems of Statistics, Schaum's Publishing Series.
W.W. Daniel : Bio Statistics : A foundation for Analysis in the Health Sciences 7th Ed.
(1999).
Wiley Series in Probability and Statistics. Applied Probability and Statistics Section.
Paper-III :PRACTICAL-I
Maximum Marks : 100
Pass Marks
: 35%
Total Practical : 60 (of 90 minutes each)
Sessions
Time Allowed : 3 hours
Note : The Practical Question Paper will contain five questions from the following
topics. Students will be required to attempt three questions, each of 20 marks. Viva
voce will carry 15 marks and record of the year will carry 25 marks.
LIST OF PRACTICALS:
1.
Presentation of data by Frequency tables , diagrams and graphs.
2.
Calculation of Measures of central tendency, dispersion, skewness and
Kurtosis.
3.
Product Moment Correlation .
4.
Linear Regression of two variables.
5.
Fitting of Curves (reducible to linear form) by the least square method.
6.
Spearman's Rank correlation.
7.
Multiple and Partial correlations.
8.
Fitting of Binomial , Poisson & Normal distributions.
SYLLABUS
B.A./B.Sc. (Statistics) Part – II
For Examination of Session 2010, 2011 & 2012
Paper- I: STATISTICAL MATHODS
Max. Marks : 100
Pass Marks : 35%
Total Lectures : 120 Periods (of 45 minutes each)
to be delivered
Time Allowed
: 3 hours
INSTRUCTIONS FOR THE PAPER SETTER
The question paper will consist of five sections : A, B, C, D and E. Sections A, B, C and D
will have two questions each from the respective sections of the syllabus and will carry 20 marks each
.Section E will consist of one question having 8/10 objective/very short-answer type questions
covering the entire syllabus uniformly .All the questions from the sections A ,B ,C ,D and E will carry
equal marks.
INSTRUCTIONS FOR THE CANDIDATES
Candidates are required to attempt one question each from the sections A, B, C and D of the
question paper and the entire section E. All questions will carry equal marks.
SECTION - A
Concept of a statistic and its sampling distribution. Point estimate of a parameter, concept of
unbiasedness, consistency, efficiency and sufficiency (only the definitions and examples). Maximum
likelihood estimation (standard distributions) ,Standard error of sample mean and sample proportion.
SECTION-B
Sampling distribution of sum of independent Binomial and Poisson variables. Independence of sample
mean and variance in random sampling from a normal distribution (without derivation).
Derivation of sampling distributions of chi-square, t and F distributions and their
relationships.
SECTION -C
Statistical tests and interval estimation :Null and alternative hypotheses, two types of errors and pvalue. Testing for the mean and variance of a normal distribution, testing of equality of means and
variances of two univariate normal distributions, and their related confidence intervals. Testing the
significance of sample correlation coefficient.
SECTION-D
Large sample tests : use of central limit theorem for testing and interval estimation of a single mean
and a single proportion, difference of two means and two proportions. Fisher's Z- transformation and
its uses. Chi-square test for goodness of fit and testing of independence of attributes. Yate's correction
,.
TEXT BOOKS
1.
Goon, A.M., Gupta
Fundamental of Statistics. Vol. 1. 1991, world
M.K., Dasgupta, B.
Press. Calcutta.
2.
Miller,I and Miller,M.(2002): Freund J.E. (2001)'s Mathematical statistics, ( 6th edition , low
price edition ).Prentice Hall of India .
1.
2.
3.
RECOMMENDED READINGS
Bhat B.R, Srivenkatramana T and Rao Madhava K.S. (1997): Statistics : A
Beginner's Text, Vol, I , New Age International (P) Ltd.
Mood A.M. Graybill F.A. and Boes D.C. (1974) : Introduction to the Theory of
Statistics, McGraw Hill.
Snedecor G.W and Cochran W.G. (1967) : Statistical Methods. Lowa State University Press .
Paper-II : SAMPLE SURVEYS , DESIGN AND ANALYSIS OF EXPERIMENTS
Max. Marks : 100
Pass Marks : 35%
Total Lectures : 120 Periods (of 45 minutes each)
to be delivered
Time Allowed
: 3 hours
INSTRUCTIONS FOR THE PAPER SETTER
The question paper will consist of five sections : A, B, C, D and E. Sections A, B, C and D
will have two questions each from the respective sections of the syllabus and will carry 20 marks each
.Section E will consist of one question having 8/10 objective/very short-answer type questions
covering the entire syllabus uniformly .All the questions from the sections A ,B ,C ,D and E will carry
equal marks.
INSTRUCTIONS FOR THE CANDIDATES
Candidates are required to attempt one question each from the sections A, B, C and D of the
question paper and the entire section E. All questions will carry equal marks.
SECTION-A
Concepts of population and sample, need for sampling, census and sample surveys, basic concepts in
sampling. Sample selection and sample size. Sampling and non-sampling errors. Some basic sampling
methods for estimating population mean , variance and standard error of its estimate ;simple random
sampling (SRS) with and without replacement .
SECTION-B
Stratified random sampling ; Systematic sampling ,Ratio and regression methods of estimations under
SRSWOR.
SECTION-C
Linear models : Concept of fixed effect, random effect and mixed effect models. Analysis of variance
for one way, two way classification with one observation per cell and two way classified data with
multiple but equal observations per sell under the fixed effect models .Need for design of experiment ,
fundamental principles of design .
SECTION-D
Basis designs –CRD, RBD, LSD and their analysis . Factorial Experiments : Concept of mean effects
and interactions in 2 2 & 2 3 – factorial experiments . Yates methods of computing factorial effects in
2 2 & 2 3 experiments .
TEXT BOOKS:
1
Goon A.M.,Gupta M.K.,Das Gupta. B.(1986):Fundamentals of Statistics,Vol. II World
Press,Calcutta.
2.
Singh Daroga. & Chaudhary, F.S.(1986): Theory and Analysisof Sample
Designs.
1.
REFERENCE READINGS
Sukhatme P.V. & B. V (1984) Sample Survey methods and its
Society of Agricultural Statistics..
Survey
Applicationsm Indian
2.
Murthy M.N (1967): Sampling theory and Methods, Statistical Publishing Society ,
Calcutta.
3.
Sampath S. (2000) Sampling theory and Methods, Narosa Publishing House .
4.
Das, M.N.& Giri, N.C.(1986) : Design and Analysis of experiment, Springer Verlag .
Cochran W.G. and Cox G. M. (1957): Experiment Designs, John Wiley and Sons.
Paper-III :PRACTICAL-II
Maximum Marks : 100
Pass Marks
: 35%
Total Practical : 60 (of 90 minutes each)
Sessions
Time Allowed : 3 hours
Note : The Practical Question Paper will contain five questions from the following
topics. Students will be required to attempt three questions, each of 20 marks. Viva
voce will carry 15 marks and record of the year will carry 25 marks.
LIST OF PRACTICALS:
1. Drawing random samples from standard distribution uniform, exponential &
normal.
2. Tests of significance based on t , chi square , and F for one sample , two
sample & paired sample problems ; significance of correlation coefficient ,
Use of Z transformation for testing  = 0 & 1 = 2 .
3. Large sample tests for means and proportions, tests of goodness of fit and
independence of attributes in contingency tables.
4. Selection of sample and determination of sample size, Simple random
sampling (SRS); Stratified SRS, allocation problems in stratified SRS;
Systematic Sampling, Ratio and Regression methods of estimation in SRS.
5. Analysis of variance for one-way and two-way classifications. Analysis of
CRD, RBD, and LSD.
6. Analysis of 2 2 & 2 3 factorial experiments in randomized blocks .