Download JNTUK (Jawaharlal Nehru Technological University Kakinada (JNTU kakinada)) M.Tech (ME is Master of Engineering) 2020 R19 CSE Mathematical Fndation of Computer Science Model Previous Question Paper
(M19CST1101)
I M. Tech I SEMESTER (R19) Regular Examinations
Model Question Paper
Subject: Mathematical Fndation of Computer Science
(For CST )
Time: 3 Hrs Max. Marks 75
Answer ONE question from EACH UNIT
All questions carry equal marks
CO KL M
UNIT - I
1 a)
Suppose ?? ?? =
?? 3
?? ?? ?? ?? ?? = 1,2,3????? the probability function of a random
variable X , then (i) determine the value of c (ii) find the distribution function of X
&?? (?? ? 3)
CO1 K2 7
b) The joint probability function of two discrete random variables X and Y is given by
f(x,y) = c (2x +y) where X and Ycan assume all integers such that 0 ? x ? 2, 0 ? y ?3
and f(x,y) =0 other wise. Find i) the value of c ii) E (X) iii) E(Y) iv) Var(X) and
Var(Y).
CO1 K3 8
(OR)
2 a)
Let X and Y have joint density function ?? ?? ,?? =
2?? ? ?? +??
?? ?? ?? ?? ? 0;?? ? 0
0 ?? ?? ??? ?? ?? ?? ?? ??
Then find conditional expectation of(i) Y on X (ii) X on Y
CO2 K1 8
b) CO2 K2 7
UNIT - II
3 a) It has been claimed that in 60% of all solar installations?utility bill reduced to by one-
third.Accordingly, what are probabilities utility bill reduced to by at least one- third
(i) in fr of five installations and (ii) at least fr of five installations
CO2 K2 8
b) Derive the mean, variance, coefficient skewness& kurtosis for Poisson?s distribution CO2 K3 7
(OR)
4 a) If 20% of memory chips made in a certain plant are defective, then what are the
probabilities, that a randomly chosen 100 chips for inspection (i) at most 15 will
defective (ii) at least25 will be defective (iiiin between 16 and 23 will be defective
CO2 K2 8
b) Derive the mean and variance of Exponential distribution. CO2 K3 7
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1
(M19CST1101)
I M. Tech I SEMESTER (R19) Regular Examinations
Model Question Paper
Subject: Mathematical Fndation of Computer Science
(For CST )
Time: 3 Hrs Max. Marks 75
Answer ONE question from EACH UNIT
All questions carry equal marks
CO KL M
UNIT - I
1 a)
Suppose ?? ?? =
?? 3
?? ?? ?? ?? ?? = 1,2,3????? the probability function of a random
variable X , then (i) determine the value of c (ii) find the distribution function of X
&?? (?? ? 3)
CO1 K2 7
b) The joint probability function of two discrete random variables X and Y is given by
f(x,y) = c (2x +y) where X and Ycan assume all integers such that 0 ? x ? 2, 0 ? y ?3
and f(x,y) =0 other wise. Find i) the value of c ii) E (X) iii) E(Y) iv) Var(X) and
Var(Y).
CO1 K3 8
(OR)
2 a)
Let X and Y have joint density function ?? ?? ,?? =
2?? ? ?? +??
?? ?? ?? ?? ? 0;?? ? 0
0 ?? ?? ??? ?? ?? ?? ?? ??
Then find conditional expectation of(i) Y on X (ii) X on Y
CO2 K1 8
b) CO2 K2 7
UNIT - II
3 a) It has been claimed that in 60% of all solar installations?utility bill reduced to by one-
third.Accordingly, what are probabilities utility bill reduced to by at least one- third
(i) in fr of five installations and (ii) at least fr of five installations
CO2 K2 8
b) Derive the mean, variance, coefficient skewness& kurtosis for Poisson?s distribution CO2 K3 7
(OR)
4 a) If 20% of memory chips made in a certain plant are defective, then what are the
probabilities, that a randomly chosen 100 chips for inspection (i) at most 15 will
defective (ii) at least25 will be defective (iiiin between 16 and 23 will be defective
CO2 K2 8
b) Derive the mean and variance of Exponential distribution. CO2 K3 7
2
UNIT - III
5 a)
The following shows corresponding values of three variables X,Y,Z. Find least square
regression equation Z= a+bx+cy
x 1 2 1 2 3
y 2 3 1 1 2
z 12 19 8 11 18
CO4 K3 8
b) Explain the procedure for fitting an exponential curve of the form y = ae
bx
. CO4 K2 7
(OR)
6 a) What the properties of a good estimator. Explain each of then CO3 K1 7
b) Suppose that n observations ?? 1,
?? 2???
?? ?? ?? ?? ?? ?? ?? ?? ?? from normal distribution and
variance is unknown. Find the maximum likelihood estimate of the mean.
CO3 K3 8
UNIT ? IV
7 a) Prove that in any non- directed graph there is even number of vertices of odd degree. CO4 K1 8
b) State and prove Euler?s formula for planar graphs CO4 K2 7
(OR)
8 a) Prove that a tree with ?n? vertices have ?n-1? edges CO4 K3 7
b)
If T is a binary tree of n vertices,show that the number of pendant vertices is
?? +1
2
CO4 K1 8
UNIT ? V
9 a) Using the principles of Inclusion and exclusion find the number of integers between 1
and 100 that are divisible by 2 ,3 or 5
CO5 K3 7
b) Find the number of integral solutions for ?? 1
+ ?? 2
+ ?? 3
+ ?? 4
+ ?? 5
= 50where?? 1
?
4, ?? 2
? 7, ?? 3
? 14, ?? 4
? 10, ?? 5
? 0
CO5 K2 8
(OR)
10
a)
Solve the recurrence relation 0 12 7
2 1
? ? ?
? ? n n n
a a a for n 2 ? using Generating
function method.
CO5 K2 8
b)
Solve
n
n n n
a a a 4 10 7
2 1
? ? ?
? ?
for n 2 ? .
CO6 K2 7
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This post was last modified on 28 April 2020