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Reg No.: Name:

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

Course Code: MA202
Course Name: PROBABILITY DISTRIBUTIONS, TRANSFORMS AND NUMERICAL
METHODS
Max. Marks: 100 Duration: 3 Hours

Normal distribution table is allowed in the examination hall.

PART A (MODULES I AND II)
Answer two full questions.

1 a) Suppose that the probabilities are 0.4, 0.3, 0.2, and 0.1 that there will be 0, 1, 2, 03 (7)
power failures in a certain city during the month of July. Find the mean and
variance of this probability distribution.

b) During one stage in the manufacture of integrated circuit chips, a coating must be (8)
applied. If 70%of chips receive a thick enough coating. Use Binomial distributionto
find the probabilities that, among 15 chips
(i) atleast 12 will have thick enough coating;
(ii) at most 6 will have thick enough coating;
(iii) exactly 10 will have thick enough coating.
2 a) Ifthe distribution function of a random variable is given by (7)
7 1೨೫3, for ೫೨1
27(0- ‏پر‎
‎0 for ೫51
find the probabilities that this random variable will take on a value
(i) less than 3; (ii) between 4 and 5.
b) Ina given city, 6% of all drivers get at least one parking ticket per year. Use the (8)
Poisson approximation to the binomial distribution to determine the probabilities
that among 80 drivers(randomly chosen in the city):
(i) 4 will get at least one parking ticket in any given year;
(ii) at least 3 will get at least one parking ticket in any given year;
(111) anywhere from 3 to 6, inclusive, will get at least one parking ticket in
any given year.

3 2) Derive mean and variance of uniform distribution. (7)
b) The time required to assemble a piece of machinery is a random variable having (8)
approximately a normal distribution with mean12.9 minutes and standard deviation
2.0 minutes. What are the probabilities that the assembly of a piece of machinery of

this kind will take
(i) at least 11.5 minutes;
(ii) anywhere from 11.0 to 14.8 minutes?

PART B (MODULES III AND IV)
Answer two full questions.

4 ⋅ ⋅ 7
a) Using Fourier cosine integral , show that [ ‏پیج‎ = oe if x >0. 0
വ്‌
9) ന്ന്‌ sinx if 0Find the Fourier sine transform of f(x) = if :
0 if ಜ್‌

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