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

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

d) Write Newton-cote's quadrature formula.

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

page of Answer sheet will lead to UMC against the Student.

3 | M - 72790

(S2)-150

This post was last modified on 04 November 2019