Reg No.: Name:

E4801

Total Pages: 2

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION, APRIL 2018

Course Code: MA202

Course Name: PROBABILITY DISTRIBUTIONS, TRANSFORMS AND NUMERICAL

Max. Marks: 100

1 a)
b)
2 a)
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3 a)
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4 a)
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5 a)
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6 a)
b)
7 a)
b)

METHODS

(Normal distribution table is allowed in the examination hall)
PART A (MODULES I AND 11)
Answer any two full questions, each carries 15 marks
Derive the formula for mean and variance of Binomial distribution.
100 fair dice are thrown. Find the expectation of the sum of the numbers thrown.
A continuous random variable X has a pdf f(x) = kx?e-*;x > 0.
Find 1) Valueofk and ii) Mean of the distribution.

If X is a uniformly distributed R V with mean 1 and variance 3 find P(|X - 2| ಆ 2)

The time in hours required to repair a machine is exponentially distributed with
mean 20. What is the Probability that the required time :
i) Exceeds 30 hrs ii) Between 16 hrs and 24 hrs.
Marks of a set of students for a certain subject are approximately normally
distributed with mean 62 and variance 9. If 4 students are randomly selected, what
is the probability that 3 of them have less than 60 marks?
PART B (MODULES III AND IV)
Answer any two full questions, each carries 15 marks

1 if |x|<1
0 if |x| < 1

Fi F ⋅ ⋅ T = co wsinwx
ind the Fourier Sine Transform of f(x) = ௪-3, Hence evaluate 0 ‏ہے‎ dw.

Find the Fourier Integral representation of f(x) = {

Find the Laplace Transform of :
(i) sin3t cos 2t (ii) € 2८८0521
Find the Inverse Laplace Transform of:
‏کہ‎ S-4 ⋅⋅ 4
(9) 52-4 (i) 52-25-3
Find the Fourier Cosine Transform of f(x) = sinx; 0 > 2 > 7.
Solve, by using Laplace Transform: y" + y 3 cos 2t; y(0) = 0,y’(0) = 0.
PART C (MODULES V AND VI)
Answer any two full questions, each carries 20 marks

Find a root lying between 0 and 2 of f (x) = cosx — 3x + 1 = 0. (correct to 3

decimal places).

Using Lagrange’s interpolation formula, fit a polynomial to the given data and
hence find y(2)

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Duration: 3 Hours

Marks

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