Jawaharlal Nehru Technological University Kakinada 2007 B.Tech Computer Science and Engineering PROBABILITY AND STATISTICS (3) - 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, info Technology
and Computer Science & Systems Engineering)
Time: three hours Max Marks: 80
ans any 5 ques.
All ques. carry equal marks
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1. (a) 2 cards are opted at random from 10 cards numbered one to 10. obtain the
probability that the sum is even if
i. the 2 cards are drawn together
ii. the 2 cards are drawn 1 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. obtain the probabilities A,B,C to be become M.D’s if bonus
scheme introduced. [5+5+6]
2. (a) 2 dice are thrown. Let X the random variable assign to every point (a,b) in
S the maximum of its numbers. obtain the distribution, the mean and variance
of the distribution.
(b) Ten coins are tossed simultaneously. obtain the probability of getting at
lowest seven heads. [8+8]
3. (a) If the variance of a poisson variate is 3. obtain the probability that
i. x=0
ii. one _ x <4
iii. 0 < x _3
(b) provided that the mean heights of students in a class is 158 cms with standard
deviation of 20cms. obtain how many students heights lie ranging from 150 cms and
170 cms, if there are 100 students in the class. [8+8]
4. Samples of size two are taken from the population 4, 8, 12, 16, 20, 24 without re-
placement. obtain
(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 stated to be drawn from a large number of bars.
Whose lengths are normally distributed with mean four feet and S.D 0.6ft. If the
sample mean is 4.2 ft, can the sample be regarded as a actually random sample?
1 of 2
(b) A random sample of 500 apples was taken from a large consignment and 60
were obtained to be bad. Within the 98% confidence limits for the percentage
number of bad apples in the consignment. [8+8]
6. The subsequent are the avg. 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 provided in the subsequent 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 eight 14 nine one 16 seven nine 12 10 13 11
(b) obtain the most plausible values of x and y
x + 2y – seven = 0 2x + 3y –2 = 0
x + 8y – three =0 3x – y + five = 0. [8+8]
8. (a) The regression equations of 2 variables x and y are
x = 0.7 y + 5.2, y = 0.3x + 2.8. obtain the mean of the variables and the
coefficient of correlation ranging from them
(b) Consider the subsequent data:
x -4 -3 -2 -1 0 one two three 4
y 0.1 2.5 3.4 3.9 4.1 3.8 3.5 2.8 0.3
obtain the correlation coefficient ‘r’. [6+10]
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Earning:   Approval pending.