Download JNTUK M-Tech 2020 R19 CSE Mathematical Fndation of Computer Science Model Question Paper

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(M19CST1101)

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I M. Tech I SEMESTER (R19) Regular Examinations

Model Question Paper

Subject: Mathematical Foundation of Computer Science

(For CST)

Time: 3 Hrs Max. Marks 75

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Answer ONE question from EACH UNIT

All questions carry equal marks

CO | KL

UNIT -1

1. a) Suppose f(x)= 3^-x for x=1,2,3....... n the probability function of a random variable X , then (i) determine the value of ¢ (ii) find the distribution function of X &P(X = 3) CO1 | K2

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2. b) The joint probability function of two discrete random variables X and Y is given by f(x,y) = ¢ (2x +y) where X and Y can assume all integers such that 0 <x <2, 0 <y <3 and f(x,y) =0 otherwise. Find 1) the value of ¢ ii) E (X) 1ii) E(Y) iv) Var(X) and Var(Y). CO1 | K3

(OR)

1. a) Let X and Y have joint density function f (x,y) = {2e^-(x+y) for x > '0,y >0 CO2 | K1 0 otherwise Then find conditional expectation of(1).Y on X (ii) X on Y
2. b) CO2 | K2

UNIT - II

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1. 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 (1) in fr of five installations and (i1) at least fr of five installations CO2 | K2
2. b) Derive the mean, variance, coefficient skewness& kurtosis for Poisson’s distribution CO2 | K3

(OR)

1. 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 least 25 will be defective (iii) in between 16 and 23 will be defective CO2 | K2
2. b) Derive the mean and variance of Exponential distribution. CO2 | K3

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UNIT - III

1. a) The following shows corresponding values of three variables X,Y,Z. Find least square regression equation Z= a+bx+cy CO4 | K3
   X 1 2 1 2 3
   

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   y 2 3 1 1 2
   z 12 | 19| 8 | 11 | 18
2. b) Explain the procedure for fitting an exponential curve of the form y = ae^mx. CO4 | K2

(OR)

1. a) What the properties of a good estimator. Explain each of then CO3 | K1

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2. b) Suppose that n observations X₁, X₂, X₃ are made from normal distribution and variance is unknown. Find the maximum likelihood estimate of the mean. CO3 | K3

UNIT - IV

1. a) Prove that in any non- directed graph there is even number of vertices of odd degree. CO4 | K1
2. b) State and prove Euler’s formula for planar graphs CO4 | K2

(OR)

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1. a) Prove that a tree with ‘n’ vertices have:n-1" edges CO4 | K3
2. b) If T is a binary tree of n vertices, show that the number of pendant vertices is i) CO4 | K1

UNIT - V

1. 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
2. b) Find the number of integral solutions for x₁ + x₂ + x₃ + x₄ + x₅ = 50 where x₁ > 4, x₂ > 7, x₃ > 4, x₄ > 0, x₅ = 0 CO5 | K2

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(OR)

1. a) Solve the recurrence relation a_n —7a_n-1+12a_n-2 =0 for n>2 using Generating function method. CO5 | K2
2. b) Solve a_n —7a_n-1 +10a_n-2 =4ⁿ for n>2. CO6 | K2