Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 5th Sem Old 151601 Computer Oriented Statistical Methods Previous Question Paper
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?V (OLD) EXAMINATION ? WINTER 2018
Subject Code:151601 Date: 30/11/2018
Subject Name: Computer Oriented Statistical Methods
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Define absolute error, relative error, truncation error and round off error.
Evaluate the sum s = ?3 + ?5 + ?7 to four significant digits and find its absolute
and relative error.
07
(b) Using Newton?s divided difference interpolation, compute the value of f(6)
from the table given below:
x 1 2 7 8
f(x) 1 5 5 4
07
Q.2 (a) Perform three steps of False Position method to find a real root of
f(x) = x
3
?2x ? 5.
07
(b) Show that the Newton-Raphson method is 2
nd
order convergent. 07
OR
(b) State Budan?s theorem. Solve x
4
- 4x
3
+ 3x
2
- 10x + 8 = 0 by Budan method, in
the interval [-1, 0] and [0, 1].
07
Q.3 (a) Solve the following system of equations by Gauss Seidel method :
x+y+54z = 110, 27x+6y-z = 85, 6x+15y+2z = 72.
07
(b) Use Lagrange?s interpolation to find the value of when x = 10 if the following
values of and are given:
x 5 6 9 11
y 12 13 14 16
07
OR
Q.3 (a) Write Gauss Elimination algorithm. Also include pivotal condensation. 07
(b) Derive the Recurrence relation for Chebyshev polynomials and using it define
?? 2( ?? ), ?? 3( ?? ) and ?? 4( ?? ).
07
Q.4 (a) Write an algorithm for cubic spline interpolation. 07
(b) Fit a second degree polynomial to the following data using least squares
method.
x 0 1 2 3 4
y 1 1.8 1.3 2.5 6.3
07
OR
Q.4 (a) Use Runge kutta method of order 4 to compute y(0.2) given that y(0) = 1, and
dy/dx = x + y
2
. Take h= 0.1
07
(b) Fit a curve of type y = ax
b
for the following data:
x 1 2 3 4
y 2.50 8.00 19.00 50.00
07
Q.5 (a) Calculate 5-yearly moving averages for the following data 07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?V (OLD) EXAMINATION ? WINTER 2018
Subject Code:151601 Date: 30/11/2018
Subject Name: Computer Oriented Statistical Methods
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Define absolute error, relative error, truncation error and round off error.
Evaluate the sum s = ?3 + ?5 + ?7 to four significant digits and find its absolute
and relative error.
07
(b) Using Newton?s divided difference interpolation, compute the value of f(6)
from the table given below:
x 1 2 7 8
f(x) 1 5 5 4
07
Q.2 (a) Perform three steps of False Position method to find a real root of
f(x) = x
3
?2x ? 5.
07
(b) Show that the Newton-Raphson method is 2
nd
order convergent. 07
OR
(b) State Budan?s theorem. Solve x
4
- 4x
3
+ 3x
2
- 10x + 8 = 0 by Budan method, in
the interval [-1, 0] and [0, 1].
07
Q.3 (a) Solve the following system of equations by Gauss Seidel method :
x+y+54z = 110, 27x+6y-z = 85, 6x+15y+2z = 72.
07
(b) Use Lagrange?s interpolation to find the value of when x = 10 if the following
values of and are given:
x 5 6 9 11
y 12 13 14 16
07
OR
Q.3 (a) Write Gauss Elimination algorithm. Also include pivotal condensation. 07
(b) Derive the Recurrence relation for Chebyshev polynomials and using it define
?? 2( ?? ), ?? 3( ?? ) and ?? 4( ?? ).
07
Q.4 (a) Write an algorithm for cubic spline interpolation. 07
(b) Fit a second degree polynomial to the following data using least squares
method.
x 0 1 2 3 4
y 1 1.8 1.3 2.5 6.3
07
OR
Q.4 (a) Use Runge kutta method of order 4 to compute y(0.2) given that y(0) = 1, and
dy/dx = x + y
2
. Take h= 0.1
07
(b) Fit a curve of type y = ax
b
for the following data:
x 1 2 3 4
y 2.50 8.00 19.00 50.00
07
Q.5 (a) Calculate 5-yearly moving averages for the following data 07
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2
Year Production Year Production
2009 464 2014 540
2010 515 2015 557
2011 518 2016 571
2012 467 2017 586
2013 502 2018 612
(b) Derive trapezoidal rule. Evaluate
6
? (1/(1+x)) dx
0
Taking n = 6, correct to four significant digits by Simpson?s 1/3
rd
rule.
07
OR
Q.5 (a) Calculate seasonal indices by the ratio-to-moving average method from the
following data:
Year
Quarter I Quarter II Quarter III Quarter IV
2016 68 62 61 63
2017 65 58 66 61
2018 68 63 63 67
07
(b) The sale of a company rose from Rs.60000 in the month of October to Rs.69000
in the month of November. The seasonal indices for these two months are 105
and 140 respectively. The owner of the company was not at all satisfied with the
rise of sales in the month of November by Rs.9000. He expected much more
because of the seasonal index for that month. What was his estimate of sales for
the month of November?
07
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This post was last modified on 20 February 2020