Annamalai University 2008-3rd Sem B.E Computer Science and Engineering , (ester) coec-302 numerical and statics methods - Question Paper
THIS ques. PAPER CONSIST OF seven PAGES...
TOTAL 5 UNITS
ans ANY 1 FULL ques. FROM every UNIT
TOTAL THERE IS 10 ques..
THIS IS 3rd SEMESTER NUMERICAL AND STATICS METHODS
Register Number:
Name of the Candidate :
6 0 6 3
B.E. DEGREE EXAMINATION, 2008
(COMPUTER SCIENCE AND ENGINEERING)
(THIRD SEMESTER)
COEC-302. NUMERICAL AND STATISTICAL METHODS
May ] [ Time: 3 Hours
Maximum : 60 Marks
Answer any ONE full question from each Unit. Use of Statistical Table is Permitted.
All questions carry equal marks.
UNIT-I
1. (a) Evaluate:
using Simpsons rule, choosing 11 ordinates.
|
x: |
4 |
6 |
8 |
10 |
|
y: |
1 |
3 |
8 |
16 |
hence, find fl(5).
2. (a) Give the data:
|
x: |
2 |
5 |
8 |
14 |
|
y: |
94-8 |
87-9 |
81-3 |
68*7 |
find y at x = 5*4.
(b) Given the data:
|
x: |
0-4 |
0-5 |
06 |
0*7 |
0*8 |
|
y: |
1*5836 |
1-7974 |
2*0442 |
2*3275 |
2*6511 |
find the first and second derivative
at x * 0-6,
3. (a) Using Regula - Falsi method, find a
positive root of x - cos x = 0.
(b) Using Crouts method, solve : x + y + 2z = 7,
3x + 2y + 4z = 13,
4x + 3y + 2z = 8.
4. (a) Using Gauss - Seidel method, solve :
4x + 2y + z = 14, x + 5y - y = 10, x + y + 8z = 20.
(b) Using Newton - Raphson method, find a positive root of xtanx = 1 *28.
UNIT-III
5. (a) Given
y = 1 + y2, y (0) = 1,
find
y(02), y(0*4) using modified Eulers method.
y" - x2 - xy, y(0) - 1, /(O) = 0, find y(0*2) by Taylor series method.
6. (a) Given
y 2e* - y, y(0) 2, y(01) = 2 010 y(0*2)=* 2*040, y(0*3) = 2*090, find y(0-4) by Milne*s method.
(b) Give
/ * y - x, y(0) = 2,
find y(0*2) by Runge - Kutta method of fourth order.
UNIT-IV
7. (a) An electrical firm manufacturing light
bulbs that have a length of life which normally distributed with mean =* 800 hrs and S.D 40 hrs. Find the probability that a bulb burns between 778 and 834 hours.
/ x : 0 < x < 1 fl[x)=<2-x : 1 < x < 2
0 : otherwise.
8. (a) The time (in hours) required to repair in machine is exponentially distributed with parameter
What is the probability that the repair
time exceeds 2 hours ? What is the conditional probability that the repair time taken at least 10 hours, given that its duration exceeds 9 hours?
(b) A continuous r.v. X follows the probability
law
f(x) Ax2, 0 < x < 1,
find A and find the probability that X lies between 0*2 and 0*5.
9. (a) Two independent random samples of 8
individuals provide the following data. Estimate the variance ratio and test the significance:
63 64 65 65 66 66 67 68
69 66 67 67 66 68 69 69
(b) A sample of 100 items is drawn from a population with mean is 162 and S.D. 416. The mean of the sample is 162*63. Does this sample mean represent a significant divergence from the population mean?
10. (a) A sample of heights of 6,400 soldiers
has a mean of 67*85 inches and a S.D. of 2*56 inches while another sample of heights of 1,600 sailers has a mean of 68*55 inches with a S.D. of 2*52 inches. Do the data indicate that the sailers are on the average taller than soldiers.
(b) The following table gives the number of aircraft accidents that occurred during the various days of the week. Find whether the accidents are uniformly distributed over the week.
|
Day |
No. of accidents |
|
Sunday |
14 |
|
Monday |
16 |
|
Tuesday |
8 |
|
Wednesday |
12 |
|
Thursday |
U |
|
Friday |
9 |
|
Saturday |
14 |
|
Attachment: |
| Earning: Approval pending. |
