[EURCS 305 / EURIT 305]
B.Tech. DEGREE EXAMINATION
III SEMESTER
PROBABILITY AND STATISTICS
(Effective from the admitted batch 2007–08)
(common for CSE & IT branches)
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) Give any two definitions of probability. State addition and
multiplication theorems on probability. 6
b) A box contains 6 red, 4 white and 5 black balls. A person
draws 4 balls from the box at random. What is the
probability that among the balls drawn, there is at least
one ball of each colour? 6
OR
2. a) Explain Binomial distribution. Give its properties. 6
b) The mean and variance of a Binomial Variate X with
parameters n and p are 16 and 8. Find P (X = 1). 6
UNIT-II
3. a) Explain Normal distribution. Give its properties. 6
b) If X follows a Rectangular distribution with mean 1 and
variance 
, then find P (X < O). 6
, then find P (X < O). 6OR
4. a) How do you fit an exponential curve Y = a e bx to the given
data? 6
b) Fit a second degree parabola to the following data: 6
| X: | 0 | 1 | 2 | 3 | 4 |
| Y: | 1 | 1.6 | 1.4 | 2.7 | 6.5 |
UNIT-III
5. a) A sample of 10 fathers and their eldest sons, has the
following data about their heights in inches:
| Father: | 65 | 63 | 67 | 64 | 68 | 62 | 70 | 66 | 72 | 71 |
| Son: | 68 | 66 | 65 | 67 | 70 | 69 | 71 | 64 | 73 | 74 |
Calculate Spearman’s Rank correlation coefficient. 6
b) Estimate the production for the year 2010, by fitting a
straight line to the following data: 6
| Year: | 2003 | 2004 | 2005 | 2006 | 2007 |
| Production: (in thousand Quintals) | 5 | 8 | 14 | 12 | 13 |
OR
6. a) Explain the concept of Standard error of a statistic. Give
Its importance. 6
b) Distinguish between Point estimation and Interval estimation. 6
UNIT-IV
7. a) Explain the terms : ( i ) Null hypothesis ( ii ) Critical region
( iii ) Level of significance, and ( iv ) Power of the test. 6
b) A coin is tossed 10,000 times and it turns up head 5,195 times.
Can the coin may be regarded as an unbiased coin? (Test at
5% level of significance) 6
OR
8. a) Before an increase in excise duty on tea, 800 persons out of
a sample of 1000 persons were found to be tea drinkers.
After an increase in excise duty, 800 persons were tea
drinkers in a sample of 1200 persons. State whether there is
a significant decrease in the consumption of tea after the
increase in excise duty? (Test at 5% level of significance). 6
b) Describe the large sample test for testing the difference
between means of two populations. 6
UNIT-V
9. a) A certain stimulus administered to each of the 12 patients
resulted the following increments of blood pressure:
| 6, | 2, | 8, | -1, | 8, | 0, | -2, | 1, | 5, | 0, | 5, | 7 |
Can it be concluded that the stimulus has significant effect in
increasing the blood pressure. 6
b) Describe the F – test for equality of variances of the two
populations. 6
OR
10. a) Describe the χ2 – test of independence of two attributes. 6
b) The following table gives the number of aircraft accidents
that occured during the seven days of the week. Test
whether the accidents are uniformly distributed over the week. 6
| Day | SUN | MON | TUE | WED | THU | FRI | SAT |
| No. of accidents | 12 | 14 | 18 | 12 | 11 | 15 | 14 |
[03-07/IIIS/107]
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