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Posted Date: 05 Feb 2008 Posted By: tarun Member Level: Silver
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2007 Jawaharlal Nehru Technological University B.E Computer Science PROBABILITY & STATISTICS SET-2 Question paper
Code No: R059210501 Set No. 2
II B.Tech I Semester Regular Examinations, November 2007
PROBABILITY AND STATISTICS
( Common to Computer Science & Engineering, Information Technology
and Computer Science & Systems Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Two cards are selected at random from 10 cards numbered 1 to 10. Find the
probability that the sum is even if
i. the two cards are drawn together
ii. the two cards are drawn one after the other with replacement.
(b) State and prove Baye’s theorem.
(c) The probabilities of A,B,C to become M.D’S of a factory are 5
10 ,
3
10 ,
2
10 . The
probabilities that bonus scheme will be introduced if they become M.D’s are
.02, 03 and .04. Find the probabilities A,B,C to be become M.D’s if bonus
scheme introduced. [5+5+6]
2. (a) Two dice are thrown. Let X the random variable assign to each point (a,b) in
S the maximum of its numbers. Find the distribution, the mean and variance
of the distribution.
(b) Ten coins are tossed simultaneously. Find the probability of getting at
least 7 heads. [8+8]
3. (a) If the variance of a poisson variate is 3. Find the probability that
i. x=0
ii. 1 x <4
iii. 0 < x 3
(b) Given that the mean heights of students in a class is 158 cms with standard
deviation of 20cms. Find how many students heights lie between 150 cms and
170 cms, if there are 100 students in the class. [8+8]
4. Samples of size 2 are taken from the population 4, 8, 12, 16, 20, 24 without re-
placement. Find
(a) mean of the population
(b) standard deviation of population
(c) the mean of sampling distribution of means
(d) standard deviation of sampling distribution of means. [16]
5. (a) A sample of 100 iron bars is said to be drawn from a large number of bars.
Whose lengths are normally distributed with mean 4 feet and S.D 0.6ft. If the
sample mean is 4.2 ft, can the sample be regarded as a truly random sample?
1 of 2
Code No: R059210501 Set No. 2
(b) A random sample of 500 apples was taken from a large consignment and 60
were found to be bad. Within the 98% confidence limits for the percentage
number of bad apples in the consignment. [8+8]
6. The following are the average weekly losses of worker hours due to accidents in 10
industrial plants before and after a certain safety programme was put into opera-
tion:
Before: 45 73 46 124 33 57 83 34 26 17
After: 36 60 44 119 35 51 77 29 24 11
Test whether the safety programme is effective in reducing the number of accidents
at the level of significance of 0.05? [16]
7. (a) The measurements of humidity and the moisture content in a raw material
are given in the following table. Fit a Straight line of the form y = ax + b
Humidity (x) 42 35 50 43 48 62 31 36 44 39 55 48
Moisture 12 8 14 9 1 16 7 9 12 10 13 11
(b) Find the most plausible values of x and y
x + 2y – 7 = 0 2x + 3y –2 = 0
x + 8y – 3 =0 3x – y + 5 = 0. [8+8]
8. (a) The regression equations of two variables x and y are
x = 0.7 y + 5.2, y = 0.3x + 2.8. Find the mean of the variables and the
coefficient of correlation between them
(b) Consider the following data:
x -4 -3 -2 -1 0 1 2 3 4
y 0.1 2.5 3.4 3.9 4.1 3.8 3.5 2.8 0.3
Find the correlation coefficient ‘r’. [6+10]
? ? ? ? ?
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