Karpaga Vinayaga College of Engineering and Technology
IAT-I ∷ 2023-24∷ODD semester
GST Road, Chinna Kolambakam – 603 308, Chengalpattu District
MCA Max. Marks 100
Semester: 04 R 2021 Date:
MA4151 : APS for CSE Time :3 Hours
Register Number
BL1 - BL3 -Applying BL5 –
Blooms Taxonomy Levels Remembering Evaluating
(BL) BL2 - BL4 – BL6 –Creating
Understanding Analyzing
Mar B C
No Part–A: Answer All Questions. 10 x 2 = 20 Marks ks L O
1 Describe QR algorithm. 2 K1 CO1
Define an inner product space. 2 K1 CO1
2
3 Define Least square method. 2 K2 CO1
4 Write down the stable formula for generalized inverse. 2 K2 CO1
2 K1 CO2
5 If is the M.G.F of X then find the mean and
variance.
If X is a Poisson variate such that P(X=2) =9 P(X=4) +90 P(X=6), find the 2 K1 CO2
6
variance.
2 K1 CO2
7 If a R.V X has the moment generating function ,
compute E
State memory less(forgetfulness)property of Exponential and Geometric 2 K2 CO2
8
1. Find the value of k if the joint pdf of (X,Y) is given by
distributions.
2 K1 CO3
9
2 K1 CO3
Given that the joint pdf of (X,Y) as
10
determine the marginal density.
Part–B: Answer All Questions. 5 x 16= 80 Marks
(i) Find the QR Decomposition for the matrix
A 16 K3 CO1
(ii) Construct a QR Decomposition for the matrix
Or
11
(i)Find the Singular value decomposition of the matrix A=
.
B 16 K3 CO1
(ii) Compute the Eigen values of the matrix
using QR factorization method.
A Find the generalized inverse of A= 16 K3 CO1
Or
12
B (i)Find the QR Decomposition for the matrix 16 K3 CO1
Obtain the Singular value decomposition of A=
(ii) .
13 (i)A random variable X has the following distribution
i. Evaluate k
ii. Evaluate P (-2<X<3)
A 16 K3 CO2
iii.Find the cumulative distribution function of X.
A.(II) Messages arrive at a switch board in a Poisson manner at an average
rate of six per hour. Find the probability for each of the following events:
(a) exactly two messages arrive within one hour, (b)no message arrives
within one hour, (c)at least three messages arrive within one hour
Or
(i)Suppose that a trainee soldier shoots a target in an independent
fashion. If the Probability that the target is shot an any one shot is 0.7.
What is the probability that the target would be hit on 10th attempt?
What is the probability that it takes him less than 4 shots?
B What is the probability that it takes him an even number of shots? 16 K3 CO2
What is the average number of shots needed to hit the target?
(ii) Find the MGF of the r.v X having the pdf f(x) = , x >0. Also
find the first four moments about the origin.
(i)For a continuous distribution, if
x 0<x≤1
f(x) = 2-x 1 ≤ x < 2
0 Otherwise
A Find the moment generating function and mean of f(x). 16 K1 CO2
(ii)Find the MGF of the r.v X having the pdf f(x) = , x >0.
Also find the first four moments about the origin.
Or
14
(i)A consulting firm rents cars from three rental agencies in the following
manner: 20% from agency D, 20% from agency E and 60% from agency
F. If 10% cars from D, 12% of the cars from E and 4% of the cars from F
have bad tyres, (i)what is the probability that the firm will get a car with
bad tyres? (ii)Find the probability that a car with bad tyres is rented from
B agency F. 16 K1 CO2
(ii)A random variable X has the following distribution
X: 0 1 2 3 4 5 6 7
2 2
P(x): 0 k 2k 2k 3k k 2k 7k2+k
i. Evaluate ‘k’
ii. Evaluate P (1.5 < X < 4.5 / X >2)
iii Find the smallest value of n for which P (X≤ n)> ½.
15 Let X and Y be two random variables having joint pmf P(x,y)= k(2x+3y),
x=0,1,2.,y=1,2,3. Find i) the marginal density functions of X and Y ii)
A 16 K3 CO3
conditional distributions of X and Y. iii) Find the probability distribution of
(X+Y).
or
(i)Find the equation of the regression lines and correlation co-efficient from
the following values of X and Y. data
X: 1 2 3 4 5
Y: 2 5 3 8 7
B (ii) In a partially destroyed laboratory record of an analysis of a correlation 16 K3 CO3
data, the following results only are legible. Variance of X is 9 and
Regression equations are 8X – 10Y+66 =0, 40X–18Y- 214=0. Find (i)
The mean values of X and Y, (ii) The S.D of Y and (iii) The coefficient of
correlation between X and Y.
KARPAGA VINAYAGA COLLEGE OF ENGINEERING AND TECHNOLOGY
CHECK LIST / DECLARATION TO BE FILLED BY THE QUESTION PAPER SETTER FOR R-2021
NAME OF THE FACULTY MEMBER : Ms.S.Maheswari
COURSE CODE & TITLE : MA4151 & APS for CSE
REGULATION : 2021
BRANCH : MCA
DATE :
1. Particulars regarding Regulations, Programme, Branch, Semester - Yes / No
Subject Code & Subject Title, Duration and Maximum Marks is clearly
printed.
2. Marks for each question and / or sub – division are clearly indicated. - Yes / No
3. Questions are evenly distributed over all the 5 units, proportionate to - Yes / No
the number of hours for each unit mentioned in the syllabus.
4. All the questions are within the prescribed syllabus. - Yes / No
5. All the figures / tables are correctly numbered and the text associated - Yes / No
with the figures / tables are readable.
6. For each Question CO, BL are clearly specified - Yes / No
7. List of Tables / Charts permitted is clearly specified. (If yes, please - Yes / No
indicate the list of tables / charts permitted in the space given below).
NAME OF THE TABLE / CHARTS: …………………………………………………Nil…………….…………………………….
Checklist of Mark Distribution:
Question Marks / CO Total Marks / BL
No. Marks
CO CO 2 CO 3 CO 4 CO 5 CO 6 L1 L2 L3 L4 L5 L
1 6
1 2 2 2
2 2 2 2
3 2 2 2
4 2 2 2
5 2 2 2
6 2 2 2
7 2 2 2
8 2 2 2
9 2 2 2
10 2 2 2
11 16 16 16
12 16 16 16
13 16 16 16
14 16 16 16
15 16 16 16
Total 40 40 20 100 14 6 80
Mark
Distributi 40% 40% 20% - - - 100 14% 6% 80%
on in (%)
Note: In the Check list of Mark Distribution, enter the marks under corresponding Bloom’s Level and Course Outcome (CO) in the
appropriate boxes.
I certify that the question paper is correct with respect to the aspects / parameters given above. The question paper may be considered for the
conduct of Model Examination.
Date: Signature:
HoD Coordinator-IQAC / NBA
