Download JNTUK (Jawaharlal Nehru Technological University Kakinada (JNTU kakinada)) M.Tech (ME is Master of Engineering) 2020 R19 IT Discrete Mathematical Structures Model Previous Question Paper
(M19IT1101)
I M.Tech I SEMESTER (R19) Regular Examinations
DISCRETE MATHEMATICAL STRUCTURES
Department of Information Technology
Time: 3 Hrs Max. Marks 75
Answer ONE question from EACH UNIT
All questions carry equal marks
CO KL M
UNIT - I
1 a) Solve for the value of c, distribution function of X and ?? ?? ? 3 , given
?? ?? =
?? 3
?? ?? ?? ?? ?? = 1,2,3????? as the probability function of the random
variable X.
CO1 K3 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 Y can assume all integers such that
0 ? x ? 2, 0 ? y ?3 and f(x,y) =0 other wise. Solve for 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 K3 7
UNIT - II
3 a) It has been claimed that in 60% of all solar installations, ?utility bill reduced
to by one- third. Identify the probabilities for the utility bill reduce by at
least one- third (i) in fr of five installations and (ii) at least fr of five
installations
CO2 K3 8
b) Utilize probability mass function of Poisson?s distribution to determine its
mean, variance, coefficient skewness & kurtosis.
CO2 K3 7
(OR)
4 a) If 20% of memory chips made in a certain plant are defective, then identify
the probabilities, that a randomly chosen 100 chips for inspection (i) at most
15 will defective (ii) at least25 will be defective (iii in between 16 and 23
will be defective
CO2 K3 8
b) Make use of pdf of the Exponential distribution to find its mean and
variance
CO2 K3 7
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1
(M19IT1101)
I M.Tech I SEMESTER (R19) Regular Examinations
DISCRETE MATHEMATICAL STRUCTURES
Department of Information Technology
Time: 3 Hrs Max. Marks 75
Answer ONE question from EACH UNIT
All questions carry equal marks
CO KL M
UNIT - I
1 a) Solve for the value of c, distribution function of X and ?? ?? ? 3 , given
?? ?? =
?? 3
?? ?? ?? ?? ?? = 1,2,3????? as the probability function of the random
variable X.
CO1 K3 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 Y can assume all integers such that
0 ? x ? 2, 0 ? y ?3 and f(x,y) =0 other wise. Solve for 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 K3 7
UNIT - II
3 a) It has been claimed that in 60% of all solar installations, ?utility bill reduced
to by one- third. Identify the probabilities for the utility bill reduce by at
least one- third (i) in fr of five installations and (ii) at least fr of five
installations
CO2 K3 8
b) Utilize probability mass function of Poisson?s distribution to determine its
mean, variance, coefficient skewness & kurtosis.
CO2 K3 7
(OR)
4 a) If 20% of memory chips made in a certain plant are defective, then identify
the probabilities, that a randomly chosen 100 chips for inspection (i) at most
15 will defective (ii) at least25 will be defective (iii in between 16 and 23
will be defective
CO2 K3 8
b) Make use of pdf of the Exponential distribution to find its mean and
variance
CO2 K3 7
2
UNIT - III
5 a) The following table shows corresponding values of three variables X, Y,Z .
Model the 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 = a e
bx
. CO4 K5 7
(OR)
6 a) What the properties of a good estimator. Explain each of them CO3 K1 7
b) Suppose that n observations ?? 1,
?? 2???
?? ?? ?? ?? ?? ?? ?? ?? ?? from normal distribution
and variance is unknown. Identify the maximum likelihood estimate of the
mean.
CO3 K3 8
UNIT ? IV
7 a) Show 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) 7
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) Make use of 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) Identify the number of integral solutions for ?? 1
+ ?? 2
+ ?? 3
+ ?? 4
+ ?? 5
=
50where?? 1
? 4, ?? 2
? 7, ?? 3
? 14, ?? 4
? 10, ?? 5
? 0
CO5 K3 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 K3 8
b)
Solve
n
n n n
a a a 4 10 7
2 1
? ? ?
? ?
for n 2 ? .
CO5 K3 7
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This post was last modified on 28 April 2020