A D1001 Pages: 2

Reg No.:_ Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION(R&S), MAY 2019

Course Code: MA202
Course Name: 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 II)
Answer two full questions.

1 a) A random variable X takes the values -3,-2,-1,0,1,2,3 such that P(X=0)=P(X>0) (7)
=P(X<0) and P(X=-3) = P(X=-2) = P(X=-1) = P(X=1) = P(X=2) = P(X=3).Obtain
the probability distribution and the distribution function of X
b) If the sum of the mean and variance of a binomial distribution for 5 trials is 1.8 (8)
Find the probability distribution function.
2 a) Itis known that 2% of the accounts in a company are delinquent. If 5 accounts are (7)
selected at random, compute the following probabilities (i) atmost 2 accounts will
be delinquent (ii) atmost 4 accounts will be delinquent
b) Find the value of k and hence find the mean and variance of the distribution (8)
f(x) = kx?e*® 03 a) If X is uniformly distributed over (-a,a) , a<0. Find o so that (i) P(x>1) = 1/3 (7)
(ii) P(|x| <1) = P(x] >1)
b) 5% of the observation in a normal distribution are below 5 and 25% of the (8)

observations are between 5 and 25. Find mean and SD

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

1-Ixl if 1151 (7)

4 a) | .
0 if IxI>1 and also find fourier

Find the fourier transform of ‏ا‎

inverse transform

b) Using fourier sine integral for f(x) = e“ show that 9 प e* (8)

5 9) Find the fourier sine transform of e*, x=0 .Hence evaluate ழ்‌ ಹ (7)

Page 1 of 2