Pages: 2

Reg No.: Name:

Time:

1,

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
M.Tech 51 (R,S) Exam Dec 2020

Cluster: Kollam
Branch: ECE
Specialisation: Communication Systems

02EC6211 RANDOM PROCESS AND APPLICATIONS
3 hours Max.Marks:60
Instructions: 411514८7 All Questions from Part A.

Answer Two Full questions from Part B.
Part A

(a) Show that when ‘n’ is very large and ‘p’ very small, the binomial distribution can
be approximated by Poisson distribution.
(b) The pdf of a random variable, X is given by

2555 ےد
‎Find the pdf of Y=3X-5‏
‎(a) If X and Y are independent and uniformly distributed RV in the interval (0,1).‏
‎Find the distribution of Z=XY‏

(a) Prove the memoryless property of geometric distribution

(0) Find ४७७ of exponential random variable. Determine the mean and variance of
exponential random variable using MGF

(a) A Gaussian random variable with variance 10 and mean 5 is transformed to

Y= 0%. Find the pdf of Y

(b) Prove Chapman-Kolmogorov Equation (4 x 9=36)
Part B

A Random Process, X(t) whose mean value is 2 and autocorrelation is
Rxx(t)= 4௪-21 is applied to ೩ system whose transfer function, H(@) = रं Find the

mean value, autocorrelation, power spectral density (PSD) and average power of
output random process.

(a) Prove Chebyshev’s inequality

(b) Let Rx(t)= ell, Find orthonormal functions, (എ) for series representation of

random process, X(t) in 0