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D192003 Pages:3

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Max. Marks: 100

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FOURTH SEMESTER B.TECH DEGREE EXAMINATION(S), DECEMBER 2019

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

Course Code: MA202

Course Name: PROBABILITY DISTRIBUTIONS, TRANSFORMS AND NUMERICAL

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METHODS

Normal distribution table is allowed in the examination hall.
PART A (MODULES I AND II)
Answer two full questions.

The following table gives the probability that a certain computer will malfunction
0, 1, 2, 3, 4, 5, or 6 times on any one day
tie ‏سا‎ रत उत क जज क रा of x 0 1 2 3 4 5 6

Malfunctions

Probability 00) | 0.17 0.29 0.27 0.16 0.07 0.03 0.01
Find (i) The Mean, Variance and Standard Deviation of this probability distribution
(ii) P(O4)

It is known that 5% of the books bound at a certain bindery have defective
bindings. Find the probability that atmost 2 of 100 book bound by this bindery will
have defective binding using

(i) The formula for binomial distribution

(ii) Poisson approximation to the binomial distribution
Derive the mean, variance and distribution function of the uniform distribution in
the interval (a,b).
The amount of time that a surveillance camera will run without having to be reset is
a random variable having the exponential distribution with mean 50 days.
Find the probability that such a camera will

(i) have to be reset in less than 20 days

(ii) not have to be reset in at least 60 days

(iii) have to be reset between 20 and 60 days.
The time required to microwave a bag of popcorn using the automatic setting can
be treated as a random variable having a normal distribution with standard
deviation 10 seconds. If the probability is 0.8212 that the bag will take less than
282.5 seconds to pop, find the probability that it will take longer than 258.3

seconds to pop.

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Duration: 3 Hours

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