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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION, JULY 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. Each carries 15 marks
1 a) A random variable X takes values 0,1, 2 and 3 with probabilities (7)
8 1 1
P(X = 0) = --, PX =1)=-, P(X = 2) = ० (+ = 3) = --
(= 0) = ट्‌, ९४ = 1) = दु, P= 2) = ‏:0م‎ = 3) =

(i) Find the mean and variance of X.
If Y = 1000 + 300X find P(Y = 1500) and E[Y]

b) या an examination, a candidate has to answer 15 multiple choice questions each of (8)
which has 4 choices for the answer. He knows the correct answer to 10 questions
and for the remaining 5 questions he chooses the answer randomly.
(i) What is the probability that he answers 13 or more questions correctly?
(ii) What is the mean and variance of the number of correct answers he gives?

2 പു The lifetime of a battery is exponentially distributed. 40% of such batteries do not (5)
last longer than 1000 hours. Mr. Kumar purchased such a battery which is already
used for 500 hours. What is the probability that it will last another 1000 hours?

b) Find the mean and variance of a random variable X which is uniformly distributed (5)

in the interval [a, b]

(c) The monthly salary (in Rs.) of 1000 employees in a factory are normally distributed (൭)
with mean 20,000 and standard deviation 5000. Estimate the number of employees
whose monthly salary will be (i) between 18,000 and 22,000 (ii) less than 18,000?

3 a) Accidents occur at an intersection at a Poisson rate of 2 per day. (7)
(i) What is the probability that there would be no accidents on a given day?
(ii) What is the probability that in January there are at least 3 days (not
necessarily consecutive) without any accidents?
b) A printer ink cartridge has a life of X hours under normal usage. The variable X is (8)
modelled by the probability density function

k
f(x) >> 72 7 x= 400,
0, otherwise.

(i) Find k

(ii) Find the probability that such a cartridge has a life of at least 600 hours of
normal usage.

(iii) Find the probability that two cartridges will have to be replaced before each
has been used for 600 hours.

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