APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER M.TECH DEGREE EXAMINATION, JULY 2018
Electronic and Communication Engineering

(SIGNAL PROCESSING)
OIEC6303 Random Processes and Applications

Time: 3 hrs Maximum marks: 60

Answer two questions from each part
Part A
1.4) State and explain Bayes' theorem in probability. (3)

b) Let X and Y are independent uniform random variables in the interval
[0,1]. Find the joint probability density function of Z and W, where
൧ and W are given as Z=X/Y and ۷۷-۶۷۰۷ (6)

2. a) Find the mean and variance of a continuous random variable with
3
moment generating function 906) = 3-५ (4)
9) The joint probability density function of two random variables X and
(ഡാ 2 0,y 2 0 0.೫72
Y is given by fxy (x, y) =

0 , otherwise

Find i) 1) P[(X+Y)<1] (5)

3. a) A continuous random variable X is described by the cumulative
distribution function

02 <
Fx(x) = kx2 5 <5 10
100k , 10
Find i) The value of 11) (3)

0) IfX is a uniform random variable in the interval [O,27t] ,then find the
probability density function of Y—cos(X) (6)