Jawaharlal Nehru Technological University Kakinada 2008 B.Tech Electronics and Communications Engineering PROBABILITY THEORY AND STOCHASTIC PROCESSES - Question Paper

x > a
= 0 x < a
obtain out variance and coe?cient of skewness. [6+10]
4. (a) Consider a probability space S = ( O, F, P). Let O = {?1....?5} = {-1, -1/2, 0,
1/2, 1} with P?i = 1/5 i = 1..5. De?ne 2 random variables on S as follows:
X(?) =? and Y(?) =?2
i. Show that X and Y are dependent random variables
ii. Show that X and Y are uncorrelated.
(b) Let X and Y be independent random variables every N (0, 1). obtain the mean
and variance of Z =(X2
+Y2
)1/2
. [8+8]
1 of 2Code No: 07A3EC10 Set No. 2
5. (a) Write the expression for expected value of a function of random variables and
prove that the mean value of a weighted sum of random variables equals the
weighted sum of mean values.
(b) X is a random variable with mean ¯ X = 3, variance s2
X = 2.
i. Determine the 2nd moment of X about origin
ii. Determine the mean of random variable y = where y = -6X +22. [8+8]
6. (a) provided X(t) = A cos ?0t + B sin ?0t where A & B are R.V’s & ?0 is a const.
S.T X(t) is Wss if A & B are uncorrelated zero mean R.V’s having di?erent
density functions but the identical variancess s2
.
(b) State the properties of cross correlation. [8+8]
7. (a) For X(t) and Y(t) are random process and prove that SXX (?) = lim t?8
E[X*
T (?)YT (?)]
2T
(b) RXY (t ) = 4u (t ) e-at
. obtain SXY (?) [12+4]
8. (a) discuss how the available noise power in an electronic circuit can be estimated.
(b) elaborate the di?erent noise sources that may be current in an electron devices?
[8+8]
? ? ? ? ?







2 of 2Code No: 07A3EC10 Set No. 3
II B.Tech I Semester Regular Examinations, November 2008
PROBABILITY THEORY AND STOCHASTIC PROCESSES
( Common to Electronics & Communication Engineering, Electronics &
Telematics and Electronics & Computer Engineering)
Time: three hours Max Marks: 80
ans any 5 ques.
All ques. carry equal marks
? ? ? ? ?
1. (a) What is sample space? discuss the Discrete sample space and Continuous
sample space with suitable example every.
(b) In a game of dice a “shooter” can win outright if the sum of the 2 numbers
showing up is either seven or 11 when 2 dice are thrown. What is his probability
of winning outright? [8+8]

Earning:   Approval pending.