Name of the University : Acharya Nagarjuna University
Degree : B.A/B.Sc Degree Examinations
Document Type : Model Question Paper
Name of the Subject : B.A/B.Sc Statistics
Website : http://www.nagarjunauniversity.ac.in/cbcs.php
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Acharya Nagarjuna B.A/B.Sc Statistics Model Question Paper
I IT,AR B.A/B,Sc STATISTICS (With Marheiatics Combination)
Paper – II
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Mathematical Expectations
Answer any FIVE questions:
Each question carries equal marks. (5 x 15 =75Marks)
l. (a) Define mathematical expectation and write ptoperties ofexpectation.
(b) State ald prove Cauchy – Schwartz inequality.
2. (a) Explain Moment Generating function and its properties.
(b) State and prove Chebychev’s inequality.
3. Define Binomial Distribution. Find the first 4 central moments of Binomial distribution.
4. Define Poisson distribution and derive recunence relation formula for moments.
5. Find the M.G.F. of Negative binomial distribution and also show that Negative binomialdistribution is a limiting case ofPoisson distribution.
6. Explain Hyper Geometric Distribution and find its mean and variance.
7. Find the C.G.F of Rectangular Distribution and also find variance of Beta 1’t kind.
8. Define Exponential Distribution and its properties
9. Derive M.G.F., Additive property and applications of Normal Distribution.
10. Define Cauchy distribution and derive its characteristic function.
Note : Compulsorv should give 2 questions from each unit.
PAPER – IV :
Statistical Inference
Arswet any FIVE ofthe following. 5 x lS = 75
1. Explain the characteristics of a good estimator.
2. State and prove Cramer – Rao inequality.
3. State and prove Nel.rnann – Pearson lemma.
4. Explain the terms
(a) Null and Alternative hypothesis
(ii) critical region and
(iii) Type-l and Type-2 enors.
5. Explain the test procedure to test the significant difference between two standard deviatiors for large samples.
6. Explain Fisher’s Z – transformation.
7. Explain t – test to test the significant difference between two means.
8. Explain chi – square test for independence ofathibutes.
9. Distinguish between parametric and non – parametric tests.
10. Explain median test.
Note : Compulsory TWO questions from each unit.
PAPER – VII(A):
Applied Statistics
Answer any FIVE of the following : 5×15=75
l. Define Time series. Explain the components of time series. Also explain the uses of time series.
2. Explain link relatives method to measue the seasonal hdices.
3. Define Index numbers. Explain the problems involved in the construction of index numbers,
4. Explain the types ofindex numbers briefly.
5. Explain about CSO.
6. Wbat do you mean by national income? And explain the methods to compute the national income.
7. Explain various mortality rat€s.
8. Explain various fertility rates.
9. Define life table. Explain the components of life tables and also obtain the relationships between them.
10. Explain the methods to measure the population growth.
Note: Compulsorv should give 2 questions from each unit.
Paper – VII(B):
Demograptty & Vital Stattstics
Answer any FIVE ofthe following. 5 x 15 = 75
1. Explain about converge and content enors in demographic data.
2. Explain about the use of balancing equations and also about the chandra sekharan – Deming formula to check the completeness ofregistration date.
3. Explain various mortality rates.
4. Explain about the use of Myer and UN indices.
5. Define life table. Explain the components of life tables and also obtain the relationships between them.
6. Explain the terms (i) Stationary and Stable population (ii) central Morrality Rate and (iiD Force of mortality.
7. Explain the consrruction of abridged life tables by King,s method and Goreville,s method.
8. Explain various birth rates.
9. Explain GRR and NRR.
10. Discuss about Crude rate of natural increase and pearle’s Vital index.
Note : Compulsory should size 2 questions from each unit.
Optimization Techniques
l. Discuss the importance ofmoders in the solution ofoperations Research problems.
2. Write the scope and applications of O.R in hdustry and business.
3. Explain (i) Linear Programing problem (ii) canonicar forrr (iii) characteristics of Standard Form ofl..p.p (iv) Slack and Surplus Variables
4. Solve the following L.p.p by Graphical Method.
Maximize Z =4\+3xz
Subject to
24 +.l; < 1000
r,+rrs800
4 < 400
:. 3 700
and x,xr20
5. State and prove Fundamental theorem ofl,.p.p.
6. Use Simplex method to solve the following L.p.p.
MaximizeZ=4xt+llxz
Subject to
2xr+xr<50
2xr+5x, Sl00
2x, +3x, <90
and xr,xr> 0
7. What is degeneracy in L.P.P. How does it resolving.
8. Explain the artificial variable technique. Use the Big M Method to solve the following
L.P.P.
Minmize Z =3\+5xz
Subject ,o
x, + xr22
x, S6
3xr+2xr=18
and xr,xr}0
9. Describe Dual Simplex procedure to solve the L.P.p.
10. Explain (i) Duality (ii) Statement of Fundamental theorem of quality
(iii) Show that tire dual of the dual is the primal linear programing problem
Note: Compulsory should give 2 Questions from each unit.