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Reg No.:___ Name:
ROT RIN

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION, DECEMBER 2018

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.

PART A
Answer any two questions

13) Ifthe random variable X takes the values 1,2,3 and 4 such that 7
2P(X=1)=3P(X=2)=P(X=3)=5P(X=4),find the probability distribution and cumulative
distribution function ofX

b) A complex electronic system is built with a certain number of backup components 8 in
itssubsystems. One subsystem has four identical components, each with a probability of 0.2
offailing in less than 1000 hours. The subsystem will operate if any two of the four
componentsare operating. Assume that the components operate independently. Find the
probability that
ijexactty two ofthe four components last longer than 1000 hours.

ii)the subsystem operates longer than 1 000 hours.
2 a) A gardener sows 4 seeds in each of 100 plant pots. The number of pots in which 7

0,1,2,3 and 4 of seeds germinated is given in the following table. Fit a binomial
distribution to the data

No. of seeds 2 1 |2 3 4
germinated
No. of pots 13 | 35 | 34 | 15 | 3
b) Find the mean and variance for the pdf 8100 1൧, 0೪೫೪1

O, elsewhere

3 a) If a random variable X has the exponential distribution with mean h, calculate the 7
probabilities that 1) > will lie between I and 3 11) X is greater than 0.5 111) X 18 atmost
4

0) In a normal distribution, 10% of the items are below 55 and 20% are above 59. 8 Find

the mean and standard deviation of the distribution. What percentage of the items are

above 60?

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