Official Statistics & Numerical Methods B.Sc Question Paper : mlsu.ac.in
University : Mohan Lal Sukhadia University
Degree : B.Sc
Department : Statistics
Subject : Official Statistics & Numerical Methods
Year : I
Document Type : Question Paper
Website : mlsu.ac.in
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Official Statistics & Numerical Methods Question :
First Year Examination of the Three Year Degree Course, 2001
(For Science and Commerce)
Paper III : (Official Statistics and Numerical Methods)
Related : Mohan Lal Sukhadia University Statistical Methods B.Sc Question Paper : www.pdfquestion.in/5828.html
Time : 3 Hours
[ Maximum Marks :50]
SECTION – A
1. Write a note on area and Yield statistics. 9
2. Write a note on Trade Statistics. 9
3. Explain the following in the context of LPP : 3+3+3
(i) Slack and Surplus variable.
(ii) feasible solution and Basic Feasible solution.
(iii) Mathematical Form of Linear Programming Problem.
4. (a) Solve the following LPP by Simplex method.
Maximize z = 2×1 + x2 s.t. x1 – x2 £ 102×1 – x2 £ 40and x1, x2 ³ 0.
(b) Write the dual form of the following LPP :
Minimize z = 15×1 + 10 x2s.t. 3×1 + 5×2 ³ 5-5×1 – 2×2 £ – 3and x1, x2 ³ 0. 5+4
SECTION – B
5. (a) Define the operators D, E and Ñ and establish the relationship among them.
(b) Determine D3 { 1 + x) ( 1 – 3x) ( 1 + 5x)}, unity being the interval of differencing. 5+4
6. (a) Express the following function and its differences in the fraction notation f (x) = x4 – 12×3 + 42×2 – 30x + 9.(b) Prove thatúûlog ( ) log 1 ( )
7. (a) Obtain the estimate of missing figures in the following table : x : 1 2 3 4 5 6 7 8 yx : 2 4 8 – 32 – 128 256
Explain why the result differs from 16 and 64. (b) Prove the following :
Dn Ux = Ux + n – nC1 Ux + n -1 + ………… + (-1)n Ux. 5+4
SECTION – C
8. Prepare a divided difference table for the following data:
x : 1 2 4 7 12
ux : 22 30 82 106 216 9
9. State and prove Newton’s divided difference formula for interpolation. What is the necessity of such formula? 9
10. If f (x) = 1/x ; x = a, b, c, d, obtain divided differences of all possible orders.
Paper – III : Computational Techniques & Official Statistics
TIME : 3 hours
UNIT – I :
Statistical Organizations in India Central Statistical Organization, National Sample Survey Organization, their functions and publications, Agricultural Statistics, Area and Yield Statistics, Trade Statistics, Statistical Organizations in Rajasthan, their functions and publications.
UNIT – II :
Linear Programming: Definition of Linear Programming Problem (LPP), formulation of LPP, Graphical method (for two variables), Simplex computational procedure and Duality.
UNIT – III :
Theory of Finite Differences: Operator, Factorial function; Newton-Gregory’s forward and backward interpolation formulae, Estimation of missing value in equal intervals.
UNIT – IV :
Theory of divided differences and its properties, Newton’s divided difference & Lagrange’s interpolation formulae, inverse interpolation by making use of Lagrange’s formula.
UNIT – V :
Numerical Integration : Trapezoidal rule, Simpson’s 1/3 & 3/8th rule, Weddle’s rule and related problems.
Recommended Books :
1. Saxena H.C. : Finite Differences and Numerical Analysis, S.Chand & Company Ltd., New Delhi.
2. Gokhroo D.Cand Saini S.R. : Numerical Analysis (Hindi edition), Navkar Prakashan, Ajmer
3. Gokhroo D.C.and Saini S.R. : Elements of Linear Programming (Hindi and English editions), Jaipur Publishing House
4. Asthana B.N. & Srivastava S.S. : Applied Statistics of India, Chaitanya Publishing House, Allahabad.
5. Porwal L.S.and Agarwal N.P. : Applied & Economic Statistics of India (Hindi Ed.)