Hall Ticket No Question Paper Code: BCSB01
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
M.Tech I Semester End Examinations (Regular) January, 2019
Regulation: IARE-R18
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Time: 3 Hours 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
UNIT I
1. 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
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, find the probability distribution for the
number of defectives.
2. State the Multi variate and Univariate Central limit theorems and their scope of application.

An Electrical firm 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.

UNIT II
3. Define and explain the concept of maximum likelihood estimation
State the formula for rth moment and moment generating functions about the origin of the
random variable X (discrete and continuous). What do the first, second and third moments
convey.
4. Analyze the sampling distribution of difference between two averages.
Define the concept of random sample. Give the mean, variance and standard deviation of a
random sample.
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UNIT III
5. Write a note on over fitting of model assessment.
A small experiment was conducted to fit a multiple regression equation relating the yield y to
temperature x1, reaction time x2, 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
Table 1
y x1 x2 x3
7.6
8.4 1
9.2 1
10.3 1
9.8 1 1
11.1 1 1
10.2 1 1
12.6 1 1 1
Using the coded variables, estimate the multiple linear regression equation
yjx1;x2;x3 0 1x1 2x2 3x3.
6. Illustrate the steps of Principle component analysis using an example.
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 Perform the analysis of variance at the 0.05 level of significance and indicate
whether or not the mean tensile strengths differ significantly for the 6 machines.
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UNIT IV
7. Find the number of circular arrangements of S E}.
What is a planar graph. prove that the complete graph K5 and the complete bipartite graph
K3,3 are not planar.
8. Find how many natural numbers n 1000 are not divisible by any of 3 without repetitions.

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.
UNIT V
9. What is SDLC and explain any two models of software development.
What are various security threats and mechanism in Cyber space.
10. Write a note on supervised and unsupervised learning.
What is the difference between clustering and classification with examples. Name two algorithms
for each.