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Reg. No. Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION, MAY 2017

Course Code: MA204
Course Name: PROBABILITY, RANDOM PROCESSES AND NUMERICAL
METHODS (AE, EC)

Max. Marks: 100 Duration: 3 Hours

Normal distribution table is allowed in the examination hall.
PARTA
Answer any two questions.

1(8) The probability distribution of a discrete random variable X is given by

P(X =x) = ua x = 0,1,2,3,4. Find (i) the value of k,(ii) the probability that X is

=
even and (iii) E(X). (7)
(b) The probability that an electric component manufactured by a firm is defective is

0.01. Ifthe produced items are sent to the market in packets of 10, find the number of
packets containing exactly two defectives and at most two defectives in a
consignment of 1000 packets using (i) binomial distributionand (ii) Poisson
approximation to binomial distribution. (8)

2(a) Buses arrived at a specified stop at 15 minute intervals starting at 7 AM. A passenger
arrives at the stop at random time between 7 AM and 7.30 AM. Find the probability
that he waits (i) less than 5 minutes, (ii) at least 12 minutes. (7)

(b) 1000 light bulbs with mean length of life 120 days are installed in a factory. Their
length of life is assumed to follow normal distribution with S.D 20 days. How many
bulbs will expire in less than 90 days? Ifit is decided to replace all the bulbs together,
what interval should be allowed between replacements if not more than 10% should
expire before replacement? (8)

3(a) A communication system sends data in the form of packets of fixed length. Noise in
the communication channel may cause a packet to be received incorrectly. If this
happens, the packet is retransmitted. Let the probability that a packet is received
incorrectly is p. Determine the average number of transmissions that are necessary
before a packet is received correctly. (7)

(b) Suppose a new machine is put into operation at time zero. Its life time is an
exponential random variable with mean life 12 hours. (i) What is the probability that
the machine will work continuously for one day? (ii) Suppose the machine has not
failed by the end of the first day, what is the probability that it will work for the whole
of the next day? (8)

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