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

Code No: 07A3EC10 Set No. 1
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) explain Joint and conditional probability.
(b) When are 2 events stated to be mutually exclusive? discuss with an example.
(c) Determine the probability of the card being either red or a king when 1 card
is drawn from a regular deck of 52 cards. [6+6+4]
2. (a) De?ne Random variable and provide the concept of random variable.
(b) In an experiment of rolling a die and ?ipping a coin. The random variable(X)
is chosen such that:
i. A coin head (H) result corresponds to positive values of X that are
equal to the numbers that show upon the die and
ii. A coin tail (T) result corresponds to negative values of X that are equal
in magnitude to twice the number that indicates on die. Map the elements
of random variable X into points on the real line and discuss.
(c) In experiment where the pointer on a wheel of chance is spun. The possible
results are the numbers from 0 to 12 marked on the wheel. The sample
space consists of the numbers in the set {0 < S < = 12} and if the random
variable X is de?ned as X = X(S) = S2
, map the elements of random variable
on the real line and discuss. [4+6+6]
3. (a) State and prove properties of variance of a random variable.
(b) Let X be a random variable de?ned by the density function
fX(x) = (p/16)cos(px/8), -4 = x = 4
= 0, elsewhere
obtain E [3X] and E[X2
]. [8+8]
4. (a) obtain the density function of W = X + Y where the densities of X and Y are
presumed to be
fX (x) = 1
a [u (x) - u (x - a)]
fY (y) = 1
b
[u (y) - u (y - b)]
Where 0 < a < b.
(b) provided the function
G(x, y) = u (x) u (y)

1 - e-(x+y)

Show that this function satis?es the ?rst 4 properties of joint probability
distribution function but fails the ?fth one. The function is therefore not a
valid joint probability distribution function. [8+8]
1 of 2Code No: 07A3EC10 Set No. 1
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]

Earning:   Approval pending.