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B4A001 Pages: 2

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION, MAY 2017

MA202: PROBABILITY DISTRIBUTIONS, TRANSFORMS AND NUMERICAL

METHODS

Max. Marks: 100 Duration: 3 Hours

Normal distribution table is allowed in the examination hall.

PART A (MODULES I AND 11)
Answer two full questions.

1. a. Given that f(x)= ‏کت‎ a probability distribution of a random variable that can take

on the values x =0,1,2,3 and 4, find k. Find the cumulative distribution function. (7)

b. If 6 of the 18 new buildings in a city violate the building code, what is the
probability that a building inspector who randomly select 4 of the new buildings will
catch

i) none of the new buildings that violate the building code
ii) one of the new buildings that violate the building code
111) at least two of the new buildings violate the building code (8)

. a. Prove that binomial distribution with parameters n and p can be approximated to

Poisson distribution when n is large and p is small with np = 4 a constant. (7)
b. Find the value of k for the probability density 7 (x) given below and hence find its
mean and variance where

(ग 0:41

0 otherwise

(8)

. 2. A random variable has normal distribution with (८ = 62.4 . Find it’s standard

deviation if the probability is 0.2 that it will take on a value greater than 79.2 (7)
b. The amount of time that a surveillance camera will run without having to be reset is
a random variable having the exponential distribution with the parameter 50 days.
Find the probability that such a camera will

i) have to be reset in less than 20 days

ii) not have to be reset in at least 60 days. (8)

PART B (MODULES III AND IV)
Answer two full questions.

7 ∙ 0 if x<0
. a. Use Fourier integral to show that | = നന്ന്‌ = a xO da = 7 if x=0 (7)
+`
° me* if x>0
x 04:41 ‏7ج‎ ⋅⋅
∣⊃⋅↧≳⊜↧⊃⊺⋐≊∁∐↥∫ (x) = ठ | as a Fourier cosine integral. (8)
x>

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