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Posted Date: 29 Nov 2008 Posted By: hari Member Level: Gold
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2005 Jawaharlal Nehru Technological University Electronics & Communications Engineering II B.Tech. I Semester Supplementary Examinations, May -2005 PROBABILITY THEORY & STOCHASTIC PROCESS Question paper
Code No: RR210403 Set No.2
II B.Tech. I Semester Supplementary Examinations, May -2005
PROBABILITY THEORY & STOCHASTIC PROCESS
( Common to Electronics & Communication Engineering and Electronics &
Telematics)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) State and prove Bayes theorem of probability.
(b) In a single throw of two dice, what is the probability of obtaining a sum of at
least 10?
2. (a) Explain the Rayleigh probability density function.
(b) Find the mean value, the mean squared value and the cumulative distribution
function for the Rayleigh distribution with parameter ¿0, specified by the
pdf f(x) = x
2 exp - 1
2
x
.
3. (a) Prove that |Rxy( )| <= sqrt[Rxx(0)Ryy(0)] .
(b) Find the mean and characteristic function of Binomial distribution.
4. (a) State the condition for wide sense stationary Random process.
(b) Find the Auto Correlation function for white noise shown in the figure below.
5. Find the input auto correlation function, output autocorrelation and o/p spectral
density of RC low pass filter, where the filter is subjected to a white noise of spectral
density N0/2.
6. (a) What are the characteristics of White noise?
(b) Discuss the spectral distribution of thermal noise.
7. (a) What are the precautions to be taken in cascading stages of a network in the
point of view of noise reduction?
(b) What is the need for band limiting the signal towards the direction increasing
SNR.
8. (a) Compare discrete and continuous channel with respect to information trans-
mission.
(b) Derive an expression for channel capacity of a continuous channel in the pres-
ence of White Gaussian noise.
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