Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (EEE)- Electrical And Electronics Engineering 2020 December 6th Sem 72790 Numerical And Statistical Methods Previous Question Paper
Total No. of Pages : 03
Total No. of Questions : 18
B.Tech. (EE) PT (Sem.?6)
NUMERICAL & STATISTICAL METHODS
Subject Code : BTEE-505
M.Code : 72790
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CAND IDAT ES :
1 .
SECT ION-A is COMPULSORY cons is ting of TEN questions carrying TWO marks
each.
2 .
SECT ION-B c ontains F IVE questions c arrying FIVE marks eac h and s tud ents
have to atte mpt any FOUR q ues tions.
3 .
SECT ION-C contains THREE questions carrying T EN marks e ach and s tudents
have to atte mpt any T WO questio ns.
SECTION-A
l.
Define relative error and give bound on the relative error of a floating point number in case
of rounding and chopping.
2.
Find the polynomial f (x) by using Lagrange's formula for the following data:
x
0
1
2
3
f (x)
1
3
9
31
3.
Define Order of convergence and give order of convergence of Bisection method.
4
Obtain the approximate value of y(0.1) for the initial value problem y = 1 + y2, y (0) = 1
with step size h = 0.1 by using Taylor series second order method.
3
1
3
5.
Evaluate the following integral
dx
using Simpson's
th rule with three sub
2
8
0 x 1
intervals.
6.
A Random variable has the following probability distribution:
x
0
1
2
3
4
p (x)
0
K
2K
2K
7K
Find K.
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7.
If X is random variable then prove that E(aX + b) = aE(X) + b, where E(X) is mathematical
expectation of X.
4
8.
If X is uniformly distributed with mean 1 and variance
then find P(X < 0).
3
9.
Show that mean of Binomial distribution is np, where n is no. of independent trails and p is
probability of success of any trail.
10. Give two properties of correlation coefficient.
SECTION-B
11. Use bisection method to find the solution of the equation 3x ? ex = 0 in the interval [1, 2]
accurate within 10?2.
12. Perform four iterations of Gauss-Seidel method using 4-digit rounding arithmetic to solve
the system of equations
4x1 + x2 + x3 = 2
x1 + 5x2 + 2x3 = ? 6
x1 + 2x2 + 3x3 = ?6
by taking initial approximation x(0) = [0.5, ?0.5, ?0.5]T.
13. Determine the largest eigenvalue and the corresponding eigenvector of the matrix
1
5
4
3
10
12
6
20
4
2
correct to three decimal places using the power method.
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2
1
1
14. Evaluate the following integral
dx
using Simpson's
rd rule with four sub
2
3
0 x 2x 10
intervals. Compare with the exact solution.
15. A random sample of 10 boys had following I.Q.'s: 70, 120, 110, 101, 88, 83, 95, 98, 107,
100. Do these data support the assumption of a population mean I.Q. of 100? Find a
reasonable range in which most of the mean I.Q. values of samples of 10 boys lie. (Given
t0.05 = 2.62 for 9 degree of freedom).
SECTION-C
16. Use Runge Kutta method of fourth order to approximate y(0.2) taking step size h = 0.1 for
dy
the initial value problem
x
y e , y(0) 0 .
dx
2
x
,
1
x 2
17. A continuous random variable X has the density function f (x) = 3
0,
elsewhere
a) Verify that f (x) is a density function.
b) Find P(0 < x < 1).
c) Find the cumulative distribution function F(x).
18. By using the method of least squares, fit a curve of the form y = axb to the following data:
x
2
3
4
5
y
27.8
62.1
110
161
NOTE : Disclosure of Identity by writing Mobile No. or Marking of passing request on any
paper of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 13 February 2021