SRI VENKATESWARA UNIVERSITY : TIRUPATI STATISTICS SYLLABUS Semester – III (CBCS Non Maths Combination BA) Paper – III : Statistical Methods ------
UNIT - I
Moments: Definition, Types of moments: Central and Non-central moments. Sheppard’s Correction for moments. Skewness and Kurtosis : Definition, Types and measures of skewness, Kurtosis with simple problems
UNIT - II
Attributes: Notations, Class, Order of class frequencies, Ultimate class frequencies, Consistency of the data, Conditions for consistency of data for 2 and 3 attributes only , Independence of attributes, Association of attributes and its measures, Contingency table and its coefficients:Square contingency(), Mean square contingency), Coefficient of mean square contingency(C), Tschuprow’s coefficient of contingency ().
UNIT – III
Curve fitting: Definition and Principals of least squares, Fitting of straight line (, Fitting of Second degree polynomial (, Fitting of power curve (and exponential curves of type i) and ii) with problems.
UNIT - IV
Correlation: Meaning, Types of Correlation. Measures of Correlation: Scatter diagram, Coefficient of correlation, Rank Correlation Coefficient(with and without ties). Linear Regression: Regression lines, Regression coefficients and its properties, Regressions lines for Un grouped data and simple problems(without proofs)
UNIT - V
Interpolation: Definition, Binomial expansion method and Graphic method. Methods of interpolation: Statement of Newton’s forward formula, Newton’s Backward formula, Lagrange’s formula and simple problems on it.
Reference Books:
1.Fundamentals of mathematical statistics: S.C.Guptha and V.K. Kapoor
2.An outlines of statistics, Vol II: Goon Guptha, M.K.Guptha and Das Guptha B
3 Basic statistics By B.N Aggrawal
4. Statistical method by S.P. Gupta
5. Fundamentals of Statistics by S.C. Gupta
4.BA/BSc II year statistics- Statistical methods and inference- Telugu Academy
5. Statistics Made simple Do it yourself on PC By K.V.S. Sarma
6. Applied Statistics with Microsoft Excel By Gerald Keller
Practicals : Paper–III - Statistical Methods
1. Calculation of Correlation coefficient for un groped data
2. Calculation of Rank Correlation coefficient with ties for un grouped data
3. Calculation of Rank correlation coefficient without ties for un grouped data
4. Construction of two regressions lines for un grouped data
95 Fitting of straight line
6. Fitting of second degree polynomial or parabola
7. Fitting of exponential curve
8 Fitting of curve
9. Fitting of power curve
10. Calculation of Yule’s coefficient of association and colligation
11.Calculation of Coefficient of mean square contingency (C), Tschuprow’s coefficient of contingency ().
12. Newton’s forward formula
13. Newton’s backward formula
14. Lagrange’s formula
Note : The above practical are to be done using M S Excel and SPSS Package where ever it is possible
Three year BA Degree Examination
CBCS – Third Semester
Part – II STATISTICS (Non - Maths)
Paper III : Statistical Methods
New Syllabus w.e.f.2015-16
Model Paper
Time : 3 hours Max. Marks :75
PART - A
Answer any FIVE questions, each question carries 5 Marks (5x5=25)
1. Explain Sheppard’s correction for moments.
2. Explain contingency table, give the specimen of 3x3 contigency table
3. Answer the following.
a) Consistency b) Ultimate Class frequency c) Manifold Classification
4. Explain the procedure to fit a straight line by the method of least squares.
5. Explain curve fitting using scattering diagram method?
6. Distinguish between correlation and regression.
7. Give the properties of regression coefficients.
8. Explain interpolation and its applications.
PART – B (5x10=50)
Answer any ONE question from each unit, each question carries 10 Marks
UNIT – I
9. Define moments and explain central and non-central moments
(or)
10 Calculate Karlpearson’s coefficient of skewness for the following data.
Marks / 0-10 / 10-20 / 20-30 / 30-40 / 40-50 / 50-60 / 60-70No. of Students / 8 / 15 / 27 / 45 / 22 / 14 / 5
UNIT – II
11 Explain conditions for consistency for three attributes
(or)
12 Calculate Yule’s coefficient of Association, coefficient of colligation for the following data.
Eye Colour in Father / Eye colour in sonNot Light / Light
Not Light / 230 / 148
Light / 151 / 471
UNIT – III
13. Explain the procedure to fit of exponential curve .
(or)
14. Fit a straight line for the following data
x / 1 / 2 / 3 / 4 / 5 / 6 / 7y / 6 / 15 / 32 / 75 / 126 / 200 / 345
UNIT – IV
15. Define a Scatter diagram and also explain various types of simple correlation.
(or)
16. Calculate Spearman’s rank correlation coefficient for the following data.
Marks in Accounts / 49 / 58 / 95 / 67 / 93 / 78 / 82 / 39 / 69Marks in Statistics / 56 / 54 / 48 / 79 / 85 / 93 / 80 / 53 / 95
UNIT – V
17. Explain interpolation by Graphical Method with a suitable example.
(or)
18. Estimate the value of ‘y’ when x=3 by using appropriate Interpolation formula from the following data
x / 2 / 4 / 6 / 8y / 16 / 256 / 1296 / 4096
SRI VENKATESWARA UNIVERSITY : TIRUPATI
STATISTICS SYLLABUS
Semester – IV (CBCS Non Maths Combination BA)
Paper – IV : Random variables and Probability distributions
------
UNIT - 1
Probability : Basic Concepts of Probability, Definitions of probability: Classical, statistical and axiomatic, Statement of Addition and Multiplication theorem on Probability for two and three events only, Statement of Baye’s theorem only. Simple problems on these topics.
UNIT – II
Random Variable: Definition, Types of random variables and its properties. Probability function: Probability mass function and Probability density function. Distribution function: Definition, Types and properties and simple problem on it
UNIT – III
Mathematical Expectation: Definition and properties, Statement and proof of Addition, Multiplication theorem on mathematical expectation for two variables only. Definitions and properties of Moment Generating Function(M.G.F), Characteristic function(C.F), Cumulant Generating Function(C.G.F), Probability Generating Function(P.G.F) without proofs
UNIT – IV
Discrete Distributions : Definition, characteristics and applications of Bernoulli Distribution, Binomial Distribution, Poisson Distribution, Negative Binomial Distribution, Geometric Distribution,. (Derivation of of Mean and variance only)
UNIT – V
Continuous Distributions : Definition, Characteristics and applications of Normal distribution, Rectangular or Uniform Distribution(Derivation of Mean and Variance), Exponential distribution(Derivation of Mean and Variance). Simple problems on normal distribution.
Reference Books:
1.Fundamentals of Mathematical Statistics: S.C.Guptha and V.K. Kapoor
2.An outlines of statistics, Vol II: Goon Guptha, M.K.Guptha and Das Guptha B
3 Basic statistics By B.N Aggrawal
4. Statistical method by S.P. Gupta
5. Fundamentals of Statistics by S.C. Gupta
4.BA/BSc II year statistics- Statistical methods and inference- Telugu Academy
5. Statistics Made simple Do it yourself on PC By K.V.S. Sarma
6. Applied Statistics with Microsoft Excel By Gerald Keller
Practicals: Paper – IV - Random variables and Probability distributions
1. Calculation of probabilities for future events by using Baye’s theorem;
2. Fitting of Binomial distribution and calculate expected frequencies (Direct method)
3. Fitting of Binomial distribution and calculate expected frequencies (Recurrence relation method)
4. Fitting of Poisson distribution and calculate expected frequencies (Direct method)
5. Fitting of Poisson distribution and calculate expected frequencies (Recurrence relation method)
6. Fitting of Negative Binomial distribution and calculate expected frequencies (Direct method)
7. Fitting of Negative Binomial distribution and calculate expected frequencies (Recurrence relation method)
8. Fitting of Geometric distribution and calculate expected frequencies ( Direct method)
9. Fitting of Geometric distribution and calculate expected frequencies (Recurrence relation method)
10. Fitting of Normal distribution and calculate expected frequencies (Ordinates method)
11. Fitting of Exponential distribution and calculate expected frequencies( Direct method)
Note : The above practical are to be done using M S Excel and SPSS Package where ever it is possible
Three year BA Degree Examination
CBCS – Forth Semester
Part – II STATISTICS (Non - Maths)
Paper IV : Radnom variables and Proability distributions
New Syllabus w.e.f. 2015-16
Model Paper
Time : 3 hours Max. Marks :75
PART - A
Answer any FIVE questions, each question carries 5 marks (5x5=25)
1. Define probability density function (pdf).
2 Define the following terms
a) Random Experiment b) Sample space c) Equally likely events.
3 Explain types of Random variable and its properties.
4 Define Mathematical Expectations and its properties
5 Define Moment generating function and its properties
6 Define poisson distribution and give its properties
7 Define Geometric distribution and also give its properties.
8 Give the applications of Normal distribution.
PART – B (5x10=50)
Answer any ONE question from each unit, each question carries 10 Marks
UNIT – I
9. State and prove Addition theorem on probability for two events.
(or)
10. A box contains 7 red, 3 green and 5 yellow balls, if 3 balls are drawn randomly from the box. Find the probability that drawn balls are of
a) different colours b) red colour
UNIT – II
11. Explain the distribution Function and also give its properties.
(or)
12. A random variable (r.v) ‘X’ has the following probability function.
X: / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7P(X): / 0 / K / 2k / 2k / 3k / K2 / 2K2 / 7K2+k
a) find ‘k’ value and b) P(x<6)
UNIT – III
13. Explain MGF and CGF and also discuss the properties.
(or)
14. Find Mean ‘E(X)’ and Variance ‘V(X)’ for the following probability distribution.
X / 0 / 1 / 2 / 3P(X) / / / /
UNIT – IV
15. Define Binomial distribution and deduce Mean and Variance.
(or)
16. Define Poisson distribution and give its properties, applications
UNIT – V
17. Define Exponential distribution and derive its Mean and Variance.
(or)
18. Define Normal distribution and also give its properties, applications