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
We rely on ads to keep our content free. Please consider disabling your ad blocker or whitelisting our site. Thank you for your support!
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.
1 | M-70558
(S2)-1073
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.
2 | M-70558
(S2)-1073
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.
3 | M-70558
(S2)-1073
This post was last modified on 13 February 2021