Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (EEE)- Electrical And Electronics Engineering 2020 December 5th Sem 70558 Numerical And Statistical Methods Previous Question Paper
Total No. of Pages : 03
Total No. of Questions : 18
B.T ech. (Electronics & Electrical Engg.) /
(Electrical Engineering & Industrial Con trol) (2012 to 2017) /
(EE) / (Electrical & Electronics Engg.) (2012 Onwards)
(Sem.?5)
NUMERICAL AND STATISTICAL METHODS
Subject Code : BTEE-505
M.Code : 70558
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CANDIDAT 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
Do all the questions :
1.
Define order of convergence for non-linear equation.
2.
Write Newton-cote's quadrature formula.
3.
Define Eigen value and Eigen vector.
4.
What is the difference between the Gauss-elimination and Gauss-Seidel methods?
5.
If a random variable X takes the values 1, 2, 3 and 4 such that
2P (X = 1) = 3P (X = 2) = P (X = 3) = 5P (X = 4), find the probability function of X.
6.
Define the condition number.
7.
Write the Newton-Raphson formula for a function f (x) = 0.
8.
Define sampling distribution.
9.
Write the probability density function for t-distribution.
10. For two lines of regression 7x ? 16y + 9 = 0 and 5y ? 4x ? 3 = 0, calculate the coefficient
of correlation.
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SECTION-B
11. Perform four iterations of the secant method to find the root of the equation xex = cos x
correct to four decimal places.
12. Find the largest Eigen value and the corresponding Eigen vector of the matrix
2
1
0
1
2
1
using Rayleigh's power method. Take [1, 0, 0]T as initial Eigen vector.
0
1
2
13. Using Newton's divided difference formula, find the missing value from the table :
x
1
2
4
5
6
y
12
15
5
--
9
14. Service calls come to a maintenance center, according to a Poisson process and, on the
average, 2.7 calls come per minute. Find the probability that (a) no more than 4 calls
come in any minute (b) fewer than 2 calls came in any minute ; (c) more than 10 calls
come in a 5-minute period.
15. A continuous random variable X has the following probability density function : f (x) = A
+ Bx, 0 x 1. If the mean of the distribution is 1 . Find the value of A and B.
2
SECTION-C
16. a) Apply Runge-Kutta fourth order method to find the approximate value of y for
dy
x = 0.2, given that
x y, and y = 1 where x = 0.
dx
b) Find by Taylor's series method, the values of y at x = 0.1 and x = 0.2 to five places of
dy
decimals from
2
x y 1, y (0) 1.
dx
17. For the following data :
x
1
3
4
8
9
11
14
y
1
2
4
5
7
8
9
Obtain :
a) Regression coefficients of y on x and x on y
b) Mean of x and y
c) Coefficient of correlation between x and y.
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18. a) A survey of 240 families with 4 children each revealed the following distribution :
No. of boys
4
3
2
1
0
No. of families
10
55
105
58
12
Is the result consistent with the hypothesis that male and female births are equally
probable? Use chi-square value for 4 & 5 d.f. at 5% level of significance is 9.49 &
11.07 respectively.
b) The intelligence quotients (IQ) of 16 students from B.Tech. IInd year showed a mean
of 107 and a standard deviation of 10, while the IQs of 14 students from B.Tech Ist
year showed a mean of 112 and a standard deviation of 8. Is there a significant
difference between the IQs of the two groups at significance levels of 0.05? Given
that critical value at 28 degree of freedom with 5% level of significance is 2.05.
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 13 February 2021