Download PTU. I.K. Gujral Punjab Technical University (IKGPTU) M.Tech. CSE 1st Semester 75153 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE Question Paper.

Roll No. Total No. of Pages : 02

Total No. of Questions : 08

M.Tech. (CSE Engg.) (2018 Batch) (Sem.?1)

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

Subject Code : MTCS-101-18

M.Code : 75153

Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

1.Attempt any FIVE questions out of EIGHT questions.

2.Each question carries TWELVE marks.

Q.l. (a) You have 800 rupees and play the following game. A box contains two white balls and

two black balls. You draw the balls out one at a time without replacement until all the

balls are gone. On each draw, you bet half of your present fortune that you will draw a

white ball. What is your expected final fortune?

(b) A number is chosen at random from the set S = {-1, 0, 1}. Let X be the number chosen.

Find the expected value, variance, and standard deviation of X.

Q.2. (a) What is the objective of Principal Components Analysis (PCA) method? Explain the

steps of PCA method in detail.

(b) What is the problem of overfitting in statistical models? How to overcome this

problem?

Q.3. Differentiate between following with the help of suitable examples:

(a) Classification and Regression

(b) Exponential families and Transformation Group families of distribution

Q.4. (a) Suppose that a connected planar graph has six vertices, each of degree four. Into how

many regions is the plane divided by a planar representation of this graph? Show that a

simple graph that has a circuit with an odd number of vertices in it cannot be colored

using two colors.

(b) Define an Euler circuit and an Euler path in an undirected graph. How can it be

determined whether an undirected graph has an Euler path and/or Euler circuit? Give

example.

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1 | M-75153 (S35)-568

Roll No. Total No. of Pages : 02

Total No. of Questions : 08

M.Tech. (CSE Engg.) (2018 Batch) (Sem.?1)

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

Subject Code : MTCS-101-18

M.Code : 75153

Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

1.Attempt any FIVE questions out of EIGHT questions.

2.Each question carries TWELVE marks.

Q.l. (a) You have 800 rupees and play the following game. A box contains two white balls and

two black balls. You draw the balls out one at a time without replacement until all the

balls are gone. On each draw, you bet half of your present fortune that you will draw a

white ball. What is your expected final fortune?

(b) A number is chosen at random from the set S = {-1, 0, 1}. Let X be the number chosen.

Find the expected value, variance, and standard deviation of X.

Q.2. (a) What is the objective of Principal Components Analysis (PCA) method? Explain the

steps of PCA method in detail.

(b) What is the problem of overfitting in statistical models? How to overcome this

problem?

Q.3. Differentiate between following with the help of suitable examples:

(a) Classification and Regression

(b) Exponential families and Transformation Group families of distribution

Q.4. (a) Suppose that a connected planar graph has six vertices, each of degree four. Into how

many regions is the plane divided by a planar representation of this graph? Show that a

simple graph that has a circuit with an odd number of vertices in it cannot be colored

using two colors.

(b) Define an Euler circuit and an Euler path in an undirected graph. How can it be

determined whether an undirected graph has an Euler path and/or Euler circuit? Give

example.

2 | M-75153 (S35)-568

Q.5. (a) Explain the use of various mathematical models and concepts for the distributed

systems in detail.

(b) How many ways are there to select four pieces of fruit from a bowl containing apples,

oranges, and pears if the order in which the pieces are selected does not matter, only the

type of fruit and not the individual piece matters, and there are at least four pieces of

each type of fruit in the bowl?

Q.6. What is Markovchain? How to specify a Markovchain? Mention the Markov property.

Q.7. (a) Consider the results of 10 tosses of a coin: H, T, T, T, T, H, T, H, T, T. Estimate the

probability of head (H) for this coin. Also, estimate the standard error of your estimate.

(b) Derive method of moments and maximum-likelihood estimators for parameter ? based

on a Poisson( ?) sample of size n.

Q.8. Write short notes on the following :

(a) Conditional expectation

(b) Probabilistic inequalities

(c) Recent trends in distribution functions

(d) Interval Estimation

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any

page of Answer Sheet will lead to UMC against the Student.

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This post was last modified on 13 December 2019