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D1002 Pages: 2

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FOURTH SEMESTER B.TECH DEGREE EXAMINATION(R&S), MAY 2019

Course Code: MA204

Course Name: PROBABILITY, RANDOM PROCESSES AND NUMERICAL METHODS

(AE, EC)

Max. Marks: 100 Duration: 3 Hours

b)
2 a)
b)
3 a)
b)

Normal distribution table is allowed in the examination hall.
PARTA
Answer any two full questions, each carries 15 marks

The probability mass function of a random variable 4 is given below:

(7)

Determine (1) the value of ८ (ii) P(X > 1)
(111) P[X > 1/)0 > X > 3)] (iv) E(X)
The probability of an item produced by a certain machine will be defective is 0.05. (8)
If the produced items are sent to the market in packets of 20, find the number of
packets containing (i) atleast 2 (ii) exactly 2 (ii) atmost 2 defective items in a
consignment of 1000 packets using Poisson distribution.

The mileage which a car owner gets with a certain kind of tyre is a random (7)
variable having an exponential distribution with mean 60,000 km Find the
probabilities that one of these tyres will last,

(a) at least 55,000 km (b) atmost 65,000 km
A random variable है follows uniform distribution in (—3,3). Find (8)
(i) P(|X| < 2) (ii) P(|X — 2| ಆ 2) (iii) P(|X| > 1)

1
(iv) the value of K for which P(X > k) = 3

Fit a binomial distribution to the following data: (7)

In an examination 30% of the candidates obtained marks below 40 and 10% of the (8)

candidates got above 75 marks. Assuming that the marks are normally

distributed, find the mean and standard deviation of the distribution.

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