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AP} ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER M.TECH DEGREE EXAMINATION,

DECEMBER 201 7 Electronics and Communication

Engineering

1. Signal Processing
2 . Microwave and TV Engineering
3. Telecommunication Engineering

01 EC6303 Random Processes and Applications

Answer any lwofull questions from each part

Marks: 60 Duration: 3 hours

PART A

a. State and prove the total probability theorem.

4 0. Let X, Y be independent random variables

with probability density 5 functions e-xu(x) and

e-yu(y) respectively. Find the joint probability
density function of ೫ = - andW = X + ४.

a. Obtain mean and moment generating function of a
Geometric 4 random variable with parameter p.

b. The joint probability density function of two
random variables X 5 and Y is given by

(१) = { 0+ छ), OS * 5
1,0 5 7 5 1

otherwise.
Find (i) the value of k
(ii) the conditional probability density
function fxx(xly)
(iii) > 0.2 y=o.7)