R09 - December, 2011 - Regular Examinations - Set - 2.

II B.Tech I Semester Examinations,December 2011
PROBABILITY AND STATISTICS
Common to ME, MECT, MEP, AME, CSE
Time: 3 hours Max Marks: 75
Answer any FIVE Questions
All Questions carry equal marks
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1. Three boys A, B, C are throwing a ball to each other. A always throws the ball to
B; B always throws the ball to C; but C is just as likely to throw the ball to B as
to A. Show that the process is Markovian. Find the transition matrix and classify
the states. Do all the states are ergodic? [15]
2. Patients arrive at a clinic in a poisson manner at an average rate of 6 per hour. The
doctor on average can attend to 8 patients per hour. Assuming that the service
time distribution is exponential, nd
(a) Average number of patients waiting in the queue.
(b) Average time spent by a patient in the clinic. [15]
3. For 20 army personal the regression of weight of kidneys (Y) on weight of heart
(X) is Y = 399 X 6.394 and the regression of weight of heart on weight of kidneys
is X = 1.212 Y 2.461. Find the correlation coe cient between the two variable
and also their means. [15]
4. (a) A random sample of 500 Apples was taken from a large consignment of 60
were found to be bad, obtain the 98% con dence limits for the percentage
number of bad apples in the consignment.
(b) Among the items produced by a factory out of 500, 15 were defective, in
another sample out of 400, 20 were defective. Test the signi cance between
the di erences of two proportions at 5% level. [15]
5. (a) Given that p(x=2)=9p(x=4) 90 p(x=46) for a Poisson variate X. Find:
i. P(x<2)
ii. p(x>4)
iii. p(x 1)
(b) In a Normal distribution exactly 7% of the items are under 35 and 89% are
under 63. Find the mean and the Standard deviataion of mark. [7 8]
6. (a) In 64 randomly selected hours of production, the mean and the standard devi-
ation of the number of acceptance pieces produced by an automatic stamping
machine are x = 1.038 and = .146.
At the .05 level of signi cance does this enable us to reject the null hypothesis
= 1.000 against the alternative hypothesis >1.000?

(b) A comapany claims that its light bulbs are superior to those of its main com-
petitor. If a study showed that a sample of 40 of its bulbs have a mean life
time of 647 hrs of continuous use with a S.D of 27 hrs. While a sample of 40
bulbs made by bits main competitor had a mean life time of 638 hrs of con-
tinuous use with a S.D of 31 hrs. Test the signi cance between the di erence
of two means at 5% level. [7 8]
7. (a) A random sample of six steel beams has a mean compressive strength of 58392
with a standard deviation of 648. Use this information at the level of signif-
icance =0.5 to test whether the true average compressive strength of the
steel from which this sample came is 58,000.
(b) For an F- distribution nd
i. F0:05 with #1 = 7 and #2 = 15
ii. F0:01 with #1 = 24 and #2 = 19
iii. F0:95 with #1 = 19 and #2 = 24
iv. F0:99 with #1 = 28 and #2 = 12 [15]
8. (a) A coin is biased in a way that a head is twice as likely to occur as a tail. If
the coin is tossed 3 times, nd the probability of getting 2 tail and 1 head
(b) If X is the continuous random variable whose density function is
f (x) = x if 0 < x < 1
=(2-x) if 1 x < 2
= 0, else where
Find E (25X2 30X ?? 5) [7 8]
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