AP] ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER M.TECH DEGREE EXAMINATION, DECEMBER 2015

Electronics And Communication Engineering

(Signal Processing)

OIEC6303 Random Process and Applications

Max Marks: 60 Duration: 3 Hours

Answer t-vvo questions from each part
PART A

, ३. Consider a discrete random variable

x
(7
1 > ६) ೫0೫
X(X) = ‏جج‎
‎Plot the cdf for p=0.6and n=4.
Find 21.5 > x < 3], P[1.2 > 5 1.8] (3)
b. Five missiles are fired against an aircraft carrier in the ocean. It takes at least
two direct hits to sink the carrier. All the five missiles are on the correct
trajectory but must get through the "point defence" guns of the carrier. The
point defence guns can destroy a missile with probability 0.9. What is the
probability that the carrier will still be afloat after the encounter? (3)

ಐ, The distribution function of a random variable X is given by
F(x) = 1-(1+x)e™ for 20. Find the density function, mean and variance of x.
(3)
2. a. State and Prove Baye's theorem (2) ட மிடி) c(X+Y) , Of-x-fl .
Find € and P(X+YSI ). Are X and Y independent? (3)
௦. Let 9 be a prescribed angle and X and Y be the random variables. Consider the
rotational transformation v = X cose + Y
sino w = X sine - 57) exp[-(x? +y’)/207] : find Y cose
If fxy(x,y) = Bs, ‏حم‎ 1/(27105) ۶۷۷ )۷,۷۵۰(
800 = [ॐ 7+ 2 5
y = sinx and ® 90೮೪1
Find fy(y). (3)

b. X and Y are independent random variables with ೫ = Y U(O, 1. Find and plot the
pdf of Z = max(X, Y). (3)

௦. Prove that if X and Y are zero mean Gaussian random distributions
Y2 will have Rayleigh distribution (3)