Probability,Statistics & Computational Techniques B.Tech Question Paper : vardhaman.org
ollege : Vardhaman College Of Engineering
Degree : B.Tech
Semester : I
Subject : Probability,Statistics & Computational Techniques
Document type : Question Paper
Website : vardhaman.org
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Vardhaman Computational Techniques Question Paper
VARDHAMAN COLLEGE OF ENGINEERING
B. Tech I Semester Supplementary Examinations
(Common to Computer Science and Engineering & Aeronautical Engineering)
Date : 07 July, 2014
Time: 3 hours
Max Marks: 75
July – 2014
Related : Vardhaman College Of Engineering Environmental Science B.Tech Question Paper : www.pdfquestion.in/6290.html
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
Unit – I
1. a) A committee consists of 9 students, two of which are from 1st year, three from 2nd year and four from 3rd year. Three students are to be removed at random. What is the chance that
i. The three students belong to different classes
ii. Two belong to the same class and the third to different class
iii. The three belong to the same class 8M
b) State the axioms of probability and define the following terms:
i. Random experiment
ii. Sample space
iii. Event 7M
2. State characteristics of normal distribution and prove any four of them. 15M
Unit – II
3. a) Explain the procedure to test significance and goodness of fit. 9M
b) From a random sample of 10 pigs fed on diet A, the increases in weight in a certain period were 10, 6, 16, 17, 13, 12, 8, 14, 15, 9 pounds. For another random sample of 12 pigs fed on diet B, the increase in the same period were 7, 13, 22, 15, 12, 14, 18, 8, 21, 23, 10, 17 lbs. Test whether diets A and B differ significantly as regards their effect on increase in weight. 6M
4. a) Two samples of size 9 and 8 gives the sum of squares of the deviations taken form the means as 160 inch2 and 91 inch2 respectively. Can this be regarded as drawn from the same population? 6M
b) Measurements on the length of a copper wire were taken in 2 experiements A and B as under. Test whether B’s measurement are more accurate than A’s. (The readings in both the cases being unbiased.
A’s measurements: 12.29 12.25 11.86 12.13 12.44 12.78 12.77 11.90 12.47
B’s measurements: 12.39 12.46 12.34 12.22 11.98 12.46 12.23 12.06 9M
5. a) Find a positive root of 3x + 1? sin x ? 0 by iteration method. 7M
b) For the following data, using Newton’s divided difference interpolation formula obtain an interpolating polynomial f (x) and hence find f (6) .
x 1 2 7 8
f (x) 1 5 5 4 6M
6. a) Compute f ‘(x) and f ”(x) at f ?16 for the following data
x 15 17 19 21 23 25
y ? x 3.873 4.123 4.359 4.583 4.796 5.8 7M
Compare with exact value. 7M
b) Find a real root of the equation 10 2x ? log x ? 7 ? 0 by Newton – Raphson method. 8M
Unit – III
7. a) Derive an equation for Trapezoidal rule. 10M
b) State the applications of Simpson’s rule. 5M
8. a) Derive an equation for Simpsons 3/8 rule. 7M
b) Use Simpson’s 1/3 rule to evaluate 2 0.6 0 e? x ? by taking n=6.
Unit – IV
9. a) By using modified Euler’s method, solve y ‘ ? log(x ? y), y(1) ? 2 at x ?1.2 and at x ?1.4 . 7M
b) By R-K method of 4th order solve ‘ 3 2 y ? x ( y ) with y(0) ?1 for y(0.2) taking h=0.1. 8M
10. Use Milne’s method, to find y(0.3) from y ‘ ? x2 ? y2 , y ?0? ?1 after computing y(-0.1), y(0.1) and y(0.2) by Taylor’s series method. 15M
December – 2013
B. Tech I Semester Supplementary Examinations,
(Regulations: VCE-R11
Probability, Statistics And Computational Techniques :
(Common to Computer Science and Engineering, Information Technology, Aeronautical Engineering & Civil Engineering)
Date : 30 December, 2013
Time : 3 Hours
Max. Marks : 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
Unit – I :
1. a) A box contains 100 cell phones, 20 of which are defective. 10 cell phones are selected for inspection. Find the probability that
i. Atleast one is defective
ii. Atleast three are defective
iii. All the ten are defective
iv. None of them are defective 8M
b) From a bag containing 4 white and 5 black balls, a man draws 3 balls at random. What are the odds in favour of they being all black? 7M
2. a) Out of 800 families with 5 children each, how many would you expect to have
i. 3 boys
ii. 5 girls
iii. Either 2 or 3 boys
iv. At least one boy 7M
b) Suppose 2% of the items of a factory are defective. Find the probability that
i. Defective items are 2
ii. At least 3 defective items 8M
Unit – II :
3. a) A random sample of size 81 was taken whose variance is 20.25 and mean is 32, construct 98% confidence interval. 7M
b) A die is thrown 264 times with the following results. Show that the die is biased
No. appeared on the die 1 2 3 4 5 6
Frequency 40 32 28 58 54 52 8M
4. a) A die was thrown 9000 times and of these 3220 yielded at 3 or 4. Test whether the die was unbiased? 7M
b) In a sample of 1000 people is Maharashtra, 540 are rice eaters and the rest are wheat eaters. Can we assume that both rice and wheat are equally popular in this state at 1% level of significance 8M
Unit – III :
5 a) Find the real root of the equation x ex – cos x = 0, using Newton Raphson method. 7M
b) Find the root of the equation x log10 x = 1.2, using False position method. 8M
6 a) Using Newton’s-Forward interpolation formula, find the number of students who obtained marks between 40 and 45 from the following table:
Marks: 30-40 40-50 50-60 60-70 70-80
No. of students: 31 42 51 35 31 8M