Rajasthan Technical University 2009-4th Sem B.Tech Computer Science and Engineering (back) Statistics and probability theory - Question Paper
Rajasthan tech. Univercity
B.Tech 2nd Year
2009
Statistics and probability theory
The candidate should ensure that this question
paper contains 5 printed pages.
410i S. & E T.
II B.E. (IV SEMESTER) (BACK) EXAMINATION, 2009
(New Four Year Semester Scheme)
[Branch: Computer Engineering]
Paper I
STATISTICS AND PROBABILITY THEORY
Time Allowed : Three Hours Maximum Marks 80
(1) No supplementary answer-book will be given to any candidate. Hence the candidates should write the answer precisely in the Main answer-book only.
(2) All the parts of one question should, be answered at one place in the answer-book. One complete question should not be answered at different, places in the answer-book.
Turn ova'
Attempt any five questions.
All questions cany equal marks.
1. (a) A bag Bt has 4 white and 3 black balls w
another bag B2 has 3 white and 5 black balls. A ball is drawn from the first bag and without noting its colour, is put into the second bag. Then a ball is drawn from the second bag. Find the probability that it is white.
(.b) In an examination with multiple choice answers each question has four choice answers, out of which one is correct. A candidate ticks his answer either by his skill or by guess or by copying from his neighbours. The probability of guess is 1/3 and that by copying is 1/6. The probability of correct answer by copying is 1/8.. If a candidate answers a question correctly, find the probability that he knew the answer. 8+8
2. (a) Find the moment generating function of
exponential distribution and hence calculate mean and variance.
(b) It is known that the probability of an item produced by a certain inachint will be defective is
0 05. If the produced items are sent to the market in packets of: 20, find the number of packets containing atmost 2 defective items in a consignment of 1000 packets usings Poisson distribution. 8+8
The distribution of weekly wages of 500 workers in a factory is normal with the mean and S.D. of Rs. 75 and Rs. 15. Find the number of workers
3. (a)
who receive weekly wages
2
4101
(i) more than Rs. 90
(ii) less than Rs. 45.
(b) A random variable X has the following probability distribution:
X : 0 1 2 .3 4 5 6 7 P(X) : Q k 2k 2k 3k 2k1 li+k Find:
(i) the value of k
8+8
4. (a) lif(t) be the probability density of time to failure T of a system and h(t) is failure rate function, find h(t) when
(ii) f(t)=A2te~k.
(b) Suppose that customers arrive at a bank according to a Poisson process with a mean rate, of 3 per minute; find the probability that during a time interval of 2 min, (i) exactly 4 customers arrive and (ii) more than 4 customers arrive. 8+8
4103 3 Turn over
5. Customers arrive at a one-man barber shop accord. to a Poisson process with a mean interarrival time of
12 min, Customers spend an average of 10 min in the barbers chair.
(a) What is the expected number of customers in the barber shop and in the queue?
(b) Calculate the percentage of time an arrival can walk straight into the barbers chair .without having to wait.
(c) How much time can a customer expect to spend in the barbers shop?
(d) What is the average time customers spend in the queue? 16
6. A car servicing station has 2 bays where service can be offered simultaneously. Because pf space limitation, only 4 cars are accepted for servicing. The arrival pattern is Poisson with 12 cars per day. The service time in both the bays is exponentially distributed with /.i=8 cars per day per bay. Find the average number of cars in the service station, the average number of cars waiting for service and the average time a car spends in the system. 16
7. An automata car station has one bay where service is done. The arrival pattern is Poisson with 4 cars/hour and may wait in the parking lot in the street if the bay is busy.
Find the time spent in the station by a car if service-time distribution is
uniform between 8 and 20 minutes
* (b) normal with mean service rate=12 min and (7=3 minutes.
(c) discrete with values equal to 4, 8 and 15 minutes with probabilities 0-2, 0-6 and 0-2 respectively. 16
8. (a) Obtain the rank correlation coefficient for the following data:
X: 68 64 75 50 64 80 75 40 55 64
Y: 62 58 68 45 81 60 68 48 50 74
(b) Use the method of least squares to fit a parabola to the following data:
x: 1 1-5 2 2-5 3 3-5 4 y: 1-1 1-3 1-6 2 2-7 3-4 4 1
8+8
4101 5 700
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