Download S.Y.B.Sc. Statistics Sem.III +IV

Syllabus of B.Sc. (Statistics) Semester III & Semester IV Syllabus effective
from June 2012-2013
VEER NARMAD SOUTH GUJARAT UNIVERSITY, SURAT
B.Sc. Semester III
STATISTICS PAPER – V
UNIT I: Random Variables, Probability Distributions and Generating Functions
 Random variables:
Discrete and Continuous
 Probability Distribution:
Probability mass function (p.m.f) and Probability density function
(p.d.f)
 Distribution function(c.d.f.)
 Properties and examples of above topics
 Mathematical expectation and their properties
 Moments:
 Raw, Central and Factorial and their relation
 Examples
 Generating functions:
 Moment generating function (m.g.f.) about origin and mean
 Factorial moment generating function
 Cumulant Generating Function (c.g.f.)
 Probability Generating Function (p.g.f.)
 Properties of above topics
 Examples of above topics
UNIT II: Measure of Central tendency and Dispersion for Discrete &
Continuous Random Variables:
 Measure of Central tendency:
 Mean, Mode, Median, Harmonic mean & Geometric mean
 Quartiles
 Examples
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 Measure of Dispersion:
Range, Quartile deviation, Mean deviation, Standard deviation
Examples
 Measure of Skewness and Kurtosis:
UNIT III: Bivariate Random Variables and Probability Distributions
 Bivariate Random Variables
 Joint, marginal and conditional p.m.f. of two random variables
 Joint, marginal and conditional p.d.f. of two random variables
 Independence of two random variables
 Examples of above topics for only continuous random variables
References:
1. Mood, Graybill and Boes : Introduction to theory of Statistics.
2. Hogg and Craig : Introduction to mathematical Statistics.
3. Gupta and Kapoor : Fundamentals of mathematical statistics.
4. Feller, W.C. (1968): An Introduction to probability theory and its
applications, John Wiley.
5. Bhatt, B.R. (1999): Modern probability theory; New Age International.
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B.Sc. Semester III
STATISTICS PAPER – VI
UNIT I: Bernoulli and Binomial Distributions:
 Bernoulli Distribution:
 Definition, Mean, Variance, M.G.F., β1, β2, 1, 2 and additive
property
 Binomial Distribution:
 Definition, Applications, Mean, Variance, M.G.F. about origin
and mean, Factorial moments, C.G.F., P.G.F., β1, β2, 1, 2 and
additive property
 Recurrence relation: For (i) Raw moments (ii) Central
moments (iii) Probability
 Limiting form
 Examples
UNIT II: Poisson and Discrete Uniform Distributions:
 Poisson Distribution:
 Definition, Applications, Mean, Variance, M.G.F. about
origin and mean, Factorial moments, C.G.F., P.G.F.,
& Additive property
 Recurrence relation: For (i) Raw moments (ii) Central
moments (iii) Probability
 Examples
 Discrete Uniform Distribution:
 Definition, Mean, Variance
 Examples
UNIT III: Hypergeometric, Geometric and Negative-Binomial Distributions:
 Hypergeometric Distribution:
 Definition, Applications, Mean, Variance
 Limiting form
 Examples
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 Geometric Distribution:
 Definition, Applications, Mean, Variance, M.G.F. about
origin
 Recurrence relation for Probability
 Examples
 Negative Binomial Distribution:
o Definition, Applications, Mean, Variance, M.G.F. about
origin, C.G.F.
o Recurrence relation for Probability
o Limiting form
o Examples
References:
1 Mood, Graybill and Boes : Introduction to theory of Statistics.
2 Hogg and Craig : Introduction to mathematical Statistics.
3 Gupta and Kapoor : Fundamentals of mathematical statistics.
4 Bhatt, B.R. (1999): Modern probability theory; New Age International.
5 Chandra, T.K. and Chatterjee, D. (2001): A first course in probability.
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B.Sc. Semester III
STATISTICS PAPER – VII
UNIT I: Normal Distribution:
 Normal Distribution:
 Definition, Applications and importance, Mean, Variance,
M.G.F. about origin and mean, Additive properties, Mean
deviation, Odd order moments about mean, C.G.F.,
Properties of normal Curves
 Recurrence relation for central moments
 Examples
UNIT II: Rectangular, Gamma and Exponential Distributions:
 Rectangular Distribution:
 Definition, Mean, Variance, M.G.F. about origin,
 Examples
 Gamma Distribution:
 Definition, Applications, Mean, Variance, M.G.F. about
origin, Additive properties, C.G.F.,
Mode
 Examples
 Exponential Distribution:
 Definition, Applications, Mean, Variance, M.G.F. about
origin,
, C.G.F.
 Examples
UNIT III: Beta Distribution of First kind and Beta Distribution of Second kind
 Beta Distribution of First kind :
 Definition, Mean, Variance, rth raw moment and hence first
four raw moments, Mode
 Examples
 Beta Distribution of Second kind :
 Definition, Mean, Variance, rth raw moment and hence
first four raw moments, Mode
 Examples
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References:
1 Mood, Graybill and Boes : Introduction to theory of Statistics.
2 Hogg and Craig : Introduction to mathematical Statistics.
3 Gupta and Kapoor : Fundamentals of mathematical statistics.
4 Johnston and Korz (1970): Distributions in Statistics
5 Stuart, G. and Ord, J.K. (1991): Advanced theory of Statistics, Vol. 2.
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B.Sc. Semester IV
STATISTICS PAPER – VIII
UNIT I: Correlation
 Meaning, Definition
 Scatter diagram, Types of correlation,
coefficient and its interpretation
 Properties

Correlation
Rank Correlation coefficient
 Examples
UNIT II: Regression
 Linear regression :
 Meaning, Definition

Fitting regression lines by principle of least squares

Regression coefficients and their properties
 Angle between two lines of regression and interpretation of
two regression lines
 Coefficient Determination
 Examples
UNIT III: Measures of Association of Attributes
 Measures of association :
 Idea of notations and terminology for classification of
attributes, Contingency table
 Types of association
 Methods of measures of association:
 Proportion method
 Method of Probability
 Yule’s Coefficient of association
 Coefficient of contingency
References:
1
2
3
4
Mood, Graybill and Boes : Introduction to theory of Statistics.
Hogg and Craig : Introduction to mathematical Statistics.
Gupta and Kapoor : Fundamentals of mathematical statistics.
Stuart, G. and Ord, J.K. (1991): Advanced theory of Statistics, Vol. 2.
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B.Sc. Semester IV
STATISTICS PAPER – IX
UNIT I: Large Sample test
 Test of significance for single proportion
 Test of significance for the difference of proportions
 Test of significance for single mean
 Test of significance for the difference of means
 Test of significance for the difference of standard devotions
 Examples
UNIT II: Small Sample test
Chi-Square Distribution
 Definition: Chi-Square variate
 Applications:
 To test the ‘goodness of fit’
 To test the independence of attributes
 To test the variance has a specified value
 Yate’s Correction
 Examples
t- distribution and F - distribution
 t- distribution:
 Definition: t- statistic
 Application:
 Test for single mean
 Test for difference of means: For independent samples and
for dependent samples
 Test the significance of an observed sample correlation
coefficient
 Examples
 F- distribution:
 Definition: F statistic
-Application:
 Test for equality of two population variances
 Examples
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UNIT III: INTERPOLTION
 Finite Differences:
 Definition of operators Δ,,E,δ,µ,D
 Relation among operators
 Finite difference table
 Divided differences
 Divided difference table
 Examples
 Interpolation:
 For equal intervals:
 Newton's forward difference interpolation formula
 Newton's backward Difference interpolation formula
 Examples
 For unequal intervals:
 Newton's divided difference interpolation formula
 Lagrange's interpolation formula
 Examples
References:
1.
2.
3.
4.
5.
Mood, Graybill and Boes : Introduction to theory of Statistics.
Hogg and Craig : Introduction to mathematical Statistics.
Gupta and Kapoor : Fundamentals of mathematical statistics.
Stuart, G. and Ord, J.K. (1991): Advanced theory of Statistics, Vol. 2.
S.S.Shastry: Numerical Analysis; Prentice Hall of India.
6. H. Freeman: Finite difference for acturial sciences.
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B.Sc. Semester IV
STATISTICS PAPER – X
UNIT I: Statistical Quality Control (SQC)
 Definition, Objectives, Advantages
 Causes of variations
 Types of Quality control
 Control Charts:
 Define: Control limits

limits
 Theory of runs
UNIT II: Types of Control Charts:
 Control charts for variables:
 Range chart
 Standard deviation chart
 Mean chart
 Examples and uses of Control charts for variables
 Control charts for attributes:
 Fraction defective chart
 Number of defectives chart
 Number of defects per unit chart
 Examples and uses of Control charts for attributes
UNIT III: Acceptance Sampling plans
 Purpose of sampling plan
 Explain: 100% inspection and Sample inspection, Producer’s
risk and Consumer’s risk, Good and bad lots, AQL, LTPD
 OC curve, Ideal OC curve
Types of Sampling Plans
 Single Sampling and Double Sampling Plans:
 Procedure
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
OC curve, ASN, AOQ and AQQL, ATI
 Examples
References:
1 Duncan, (1953): Quality control and industrial statistics.
2 R.T.Ratani: Ankdashatriya Gunavatta Niyantran (in Gujarati);
University Granth Nirman Board.
3 E.L.Grant: Statistical Quality Control, Tata McGraw Hill Co.
4 D.J. Cowden: Statistical methods in quality control; Asia Publishing
House.
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VEER NARMAD SOUTH GUJARAT UNIVERSITY, SURAT
B.Sc. Semester – III
STATISTICS PRACTICAL PAPERS – V, VI and VII
[Effective from June-2012]
Practical based on Statistics Paper V, VI and VII
B.Sc. Semester – IV
STATISTICS PRACTICAL PAPERS – VIII, IX and X
[Effective from June-2012]
Practical based on Statistics Paper VIII, IX and X
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