Download JNTU Hyderabad (Jawaharlal Nehru Technological University Hyderabad) M Tech (Master of Engineering) I Semester 2019 January Mathematical Foundation of Computer Question Paper
M.Tech I Semester End Examinations (Regular) ? January, 2019
Regulation: .?R18
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Time: 3 Hours (CSE) Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
1.
(a)
(b)
UNIT ? I
State the conditions for a function f : S ?> R , Where S is a sample Space and R is set of real
numbers, to be probability mass or distribution function of a discrete random variable. Also
state conditions for f to be probability density function of a continuous random variable [7 M]
A shipment of 8 similar micro computers to a retail outlet contains 3 that are defective. If a
school makes a random purchase of 2 of these computers, ?nd the probability distribution for the
number of defectives. [7M]
State the Multi variate and Univariate Central limit theorems and their scope of application.
[7M]
An Electrical ?rm manufactures light bulbs that have a length of life that is approximately
normally distributed, with mean equal to 800 hours and a standard deviation of 40 hours. Find
the probability that a random sample of 16 bulbs Will have an average life of less than 775 hours.
[7M]
UNIT ? II
De?ne and explain the concept of maximum likelihood estimation [7M]
State the formula for rm moment and moment generating functions about the origin of the
random variable X (discrete and continuous). What do the ?rst, second and third moments
convey. [7M]
Analyze the sampling distribution of difference between two averages. [7M]
De?ne the concept of random sample. Give the mean7 variance and standard deviation of a
random sample. [7M]
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5.
(a)
00)
UNIT ? III
Write a note on over ?tting of model assessment. [7M]
A small experiment was conducted to ?t a multiple regression equation relating the yield y to
temperature x1, reaction time 3:2, and concentration of one of the reactants x3. TWO levels of
each variable were chosen and measurements corresponding to the coded independent variables
were recorded as follows in Table 1: [7M]
Table 1
7.6 ?1 -1 -1
8.4 1 -1 -1
9.2 ?1 1 ?1
10.3 ?1 -1 1
9.8 1 1 ?1
11.1 1 -1 1
10.2 ?1 1 1
12.6 1 1 1
Using the coded variables, estimate the multiple linear regression equation
Mylxhxz?'g = 30 + 31531 + 52332 + 33153-
Illustrate the steps of Principle component analysis using an example. [7M]
Six different machines are being considered for use in manufacturing rubber seals. The machines
are being compared With respect, to tensile strength of the product. A random sample of 4 seals
from each machine is used to determine whether the mean tensile strength varies from machine
to machine. The following Table 2 are the tensile?strength measurements in kilograms per square
centimeter x 10?1. Perform the analysis Of variance at the 0.05 level of signi?cance and indicate
whether 01" not the mean tensile strengths differ signi?cantly for the 6 machines. [7 M]
' Machine
I 3 ?3 J S 6
I 7.5 15.1 16.3 '16 l 7.5 13.3
lb!) I92 |5.7 |6.7 I92 l6.2
l5.8 ?.7 ?.8 20.8 I65 I75
l8. 6 ISA I89 I89 20.5 20. l
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10.
(a)
(b)
(a)
(b)
UNIT ? IV
Find the number of circular arrangements of S = {A7 A, B, B7 C7 C7 D7 D, E7 E}. [7M]
What is a planar graph. prove that the complete graph K5 and the complete bipartite graph
K3,3 are not planar. [7M]
Find how many natural numbers n g 1000 are not divisible by any of 2, 3 without repetitions.
[7M]
Let G be a connected graph With exactly two vertices of Odd degree. Then show that there is an
Eulerian walk starting at one Of those vertices and ending at the other. [7 M]
UNIT ? V
What is SDLC and explain any two models of software development. [7M]
What are various security threats and mechanism in Cyber space. [7M]
Write a note on supervised and unsupervised learning. [7 M]
What is the difference between clustering and classi?cation with examples. Name two algorithms
for each. [7M]
? o o O o o ?
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This post was last modified on 20 January 2020