[EURCS 305/EURIT 305]
B.Tech. DEGREE EXAMINATION
CSE & IT
III SEMESTER
PROBABILITY & STATISTICS
(Effective from the admitted batch 2007–08 onwards)
Time: 3 Hours Max.Marks: 60
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Instructions: Each Unit carries 12 marks.
Answer all units choosing one question from each unit.
All parts of the unit must be answered in one place only.
Figures in the right hand margin indicate marks allotted.
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UNIT-I
1. a) What are mutually exclusive and independent events? State
Bayes theorem on probability. 6
b) A problem in statistics is given to three students A, B and C,
whose chances of solving it are 
respectively.
respectively. What is the probability that the problem will be solved? 6
OR
2. a) Explain Poisson distribution. Give its applications. 6
b) A manufacturer of cotter pins knows that 5% of his product is
defective. If he sells cotter pins in boxes of 100 and guarantees
that not more than 10 pins will be defective, what is the
probability that a box will fail to meet the guaranteed quality? 6
UNIT-II
3. a) Explain an exponential distribution. Obtain its mean and
variance. 6
b) What are the important characteristics and applications of
normal distribution? 6
OR
4. a) What is the principle of least squares? How do you fit a power
curve 
to the given data? 6
to the given data? 6 b) Fit a power curve is of the form 
to the following data: 6
to the following data: 6| X: | 1 | 2 | 3 | 4 | 5 |
| Y: | 8 | 15 | 30 | 60 | 125 |
UNIT-III
5. a) From the following data, compute the coefficient of correlation
between X and Y. 6
| No. of Items | | X Series | Y Series |
| : | 15 | 15 | |
| Arithmetic Mean | : | 25 | 18 |
| Sum of squares of deviations from mean | : | 136 | 138 |
| Sum of products of deviations of X and Y from their means | : | 122 | |
b) Fit a linear regression equation of Y on X to the following data: 6
| X: | 5 | 8 | 7 | 6 | 4 |
| Y: | 3 | 4 | 5 | 2 | 1 |
OR
6. a) Explain the terms (i) Population (ii) Sample (iii) Parameter and
(iv) Statistic. 6
b) Describe the method of Maximum likelihood estimation. 6
UNIT-IV
7. a) What are the steps involved in test of significance? 6
b) A machine puts out 16 imperfect articles in a sample of 500.
After machine is overhauled, it puts out 3 imperfect articles in
a batch of 100. Has the machine improved? 6
OR
8. a) A random sample of 400 students is found to have a mean
height of 171.38 cms. Can it be reasonably regarded as a
sample from a lalrge population with mean height 171.17 cms.
and standard deviation 3.30 cms. (Test at 5% level of
significance). 6
b) A random sample of 1200 households from one town gives the
mean income as Rs.500 per month with a standard deviation of
Rs.70 and a random sample of 1000 households from another
town gives the maximum income as Rs.600 per month, with a
standard deviation of Rs.90. Test whether the mean income of
households from two towns differ significantly or not?
(Test at 5% level of significance). 6
UNIT-V
9. a) Two independent samples of 8 and 7 items respectively had the
following values:
| Sample I | : | 9 | 11 | 13 | 11 | 15 | 9 | 12 | 14 |
| Sample II | : | 10 | 12 | 10 | 14 | 9 | 8 | 10 | |
Is the difference between the means of samples significant? 6
b) A random sample of 11 pairs of observations gives a correlation
coefficient 0.52. Is the correlation coefficient significant?
(Test at 5% level of significance). 6
OR
10. a) Describe the c2 – test of goodness of fit. 6
b) In an experiment of immunization of cattle from Tuberculosis,
the following results were obtained: 6
| | | Affected | Unaffected |
| Inoculated | : | 12 | 28 |
| Not-inoculated | : | 13 | 7 |
Examine the effect of vaccine in controlling the incidence of
the disease.
[3,7/IIIS/109]
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