PTU B.Tech Electrical Engineering 6th Semester May 2019 72790 NUMERICAL AND STATISTICAL METHODS Question Papers

PTU Punjab Technical University B-Tech May 2019 Question Papers 6th Semester Electrical and Electronics Engineering (EEE)-EE-Electrical Engineering

Roll No.
Total No. of Pages : 03
Total No. of Questions : 09
B.Tech.(EE) PT (Sem.?6)
NUMERICAL AND STATISTICAL METHODS
Subject Code : BTEE-505
M.Code : 72790
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1.
SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks
each.
2.
SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3.
SECTION-C contains T HREE questions carrying T EN marks each and students
have to attempt any T WO questions.

SECTION-A
1.
Write briefly :

a) Find the absolute and absolute errors in 6 7 8 correct to 4 significant digits.

b) Write the Newton-Raphson formula for a function f (x) = 0
5
4

c) Find the eigen values of the matrix
.
1 2

e) What is the difference between Euler's and Runge-Kutta methods for solving the
differential equations?

f) Given that f(x) = k(1/2)x, is a probability distribution for a random variable which can
take on its values x = 0, 1, 2, 3, 4, 5, 6. Find k.

g) A shipment of 7 television sets contains 2 defective sets. A hotel makes random
purchase of 3 of the sets. If x is the number of defective sets purchased by the hotel,
find the probability distribution of X.

h) The probability of bomb hitting a target is 1/5. Two bombs are enough to destroy a
bridge. If six bombs are aimed at the bridge, find the probability that the bridge is
destroyed.
1 | M - 72790

(S2)-150

i) In Poisson frequency distribution, frequency corresponding to 3 successes is 2/3 times
frequency corresponding to 4 successes. Find the standard deviation of the
distribution.

j) A computer program has produced the following output for a hypothesis-testing
problem :

Difference in sample means : 2.35

Degree of freedom : 18

Test statistics : 2.01

Find the standard error of the difference in sample means.

SECTION-B
2.
Find a real root of 2x ? log10 x = 7 correct to four decimal places using iteration method.
3.
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

4.
Using Newton's divided difference formula, evaluate f (8) given :
x
4
5
7
10
11
13

y = f (x)
48 100 294 900 1210
2028
5.
Suppose that the life length of the two bulbs B1 and B2 have distribution N (x ; 40,36)
and N (x; 45, 9) respectively. If the bulb is to be used for 45-hours period, which bulb is
to be preferred? If it is to be used for 48-hours period, which bulb is to be preferred?
Given that P(Z<0.83) = 0.7967, P(Z<1.33) = 0.9082, P (Z<1.00) = 0.8143.
6.
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 level of 0.05? Given that critical value
at 28 degree of freedom with 5% level of significance is 2.05.

2 | M - 72790

(S2)-150

SECTION-C
7.
From the given data, find :(i) the two regression equations, (ii) the coefficient of
correlation between the marks in Mathematics & Statistics, and (iii) the most likely marks
in Statikstics when the marks in Mathematics are 30.
Marks in Mathematics
25
38
35
32
31
36
29
38
34
32
Marks in Statistics
43
46
49
41
36
32
31
30
33
39
8.
Apply Runge-Kutta method to find the approximate value of y for x = 0.2 in steps of 0.1,
dy
if
2
x y , given that y = 1 where x = 0.
dx
2
1
x
9.
(a) Evaluate the integral
dx

using Simpson's 1/3rd rule. Compare the error with
3
0 1 x
the exact value.

(b) In a multiple choice examination, there are 20 questions. Each question has four
alternative answers following it and the student must select the one correct answer.
Four marks are given for the correct answer and one marks in deducted for every
wrong answer. A student must secure at least 50% of maximum possible marks to
pass the examination. Suppose that a student has not studied at all so that he decides
to select the answers to the questions on a random basis. What is the probability that
he will pass in the examination.

NOTE : Disclosure of identity by writing mobile number or making passing request on any