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Name
Reg No

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
07 THRISSUR CLUSTER
FIRST SEMESTER M.TECH. DEGREE EXAMINATION DEC 2017
Computer Science and Engineering
Computer Science and Engineering
07MA 6011 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE
Time 3 hours Max.Marks: 60
Answer all six questions. Part of each question is compulsory.
Answer either part or part of each question
Q.no. Module 1 Marks
1a Find the Range and Kernel for the linear transformation T 4
Answer b or c
b Let D where D denotes derivative transform and
I where I denotes integration transform .write the
corresponding matrix representations.
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c Diagonalize the matrix .
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Q.no.
Module 2 Marks
2a Define Haar scaling function and Haar wavelet functions and prove that they
are orthogonal
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Answer b or c
b Let x .Perform the Haar
decomposition using
⁄
⁄ and
⁄
⁄ as decomposition filters.
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c Discuss about the space spanned by scaling function bases are nested. 5
Q.no. Module 3 Marks
3a
Write
as a product of disjoint cycles.
4
Answer b or c
b Define Ring ii) Ideal iii) Integral domain and iv) Field 5
c Show that the Ring Z of integers is a Euclidean domain with the function

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Q.no. Module 4 Marks
4a Define Conditional probability of two events
ii) What is meant by weak Law of Large Numbers
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Answer b or c
b Let X1 X2 ,...... Xn be identically and independently distributed random
variable with mean 3 and varience
. If n=120 use C.L.T to estimate
P (340 where X1 X2 +...... Xn .
5
c A problem in statistics in given to three students A,B and C and the chances
for them to solve the problem are
⁄
⁄
⁄ respectively . what is the
probability that the problem will be solved if all of them try independently.
5
Q.no. Module 5 Marks
5a Define Poisson process .What is its mean and variance. 5
Answer b or c
b Babies are born in the state at the rate of one birth in every 20 minutes . the
inter arrival time follows exponential distribution . find
Expected number of births in a year .
ii) The Probability that no birth will occure in any one day.
iii) The Probability for 20 birth in 4hours given that 15 births have taken
place in the first three hours of the four hours period.
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c The transition Probability matrix of a Markov chain where n having
three states is given below
P
with initial distribution 0.2 0.1) find

ii)
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Q.no. Module 6 Marks
6a Explain the Queuing model
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Answer b or c
b In a railway marshalling yard goods train arrive at the rate of 30 trains day .
Assuming that inter arrival times follows exponential distribution and the
service time is also exponential with an average of 36 minutes, calculate
average length of non empty Queue
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ii) probability that queue size exceeds 10 .
c A city has a one person barber shop which can accommodate a maximum
of 5 customers at a time waiting and 1 getting haircut). On average
customers arrive at the rate of 8 hours and the barber takes 6 minutes for
serving each customer. It is estimated that arrival process in poisson and
service time is an exponential random variable . Find
Percentage of time the barber in idle.
ii) Expected number of customers in the barber shop.
iii) Expected number of customers waiting for a hair cut.
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