SRM University 2007 B.Tech Electronics and Communications Engineering Bank of EC306-Information Theory - Question Paper
Wednesday, 30 January 2013 11:30Web
Page 2 of 7
4. a) a certain noise function follows the pdf provided by f(x)=Ae-B?x?,-? < x < ?.Determine
the relationship ranging from A and B.
b) The CDF of a certain random variable is provided as,
F(X) = 0 ; -? < X < 0,
X2/50; 0< X ?10,
50X; 10 < X? ?
Find P(X?5), P (5 < X?7) and PDF.
5. a. Determine whether the function provided by the subsequent expression is a density
function.
F(X) = 0; X < 5
(1/18) (3+2X); 5 ?X ?8
0; X > 8
b) Determine whether the function provided in the subsequent expression is CDF.
F(X) = 0; X < a
½ (X/a + 1); -a ? X ?a
1; X > a
6. a)The random variable Y is a function of a different random variable X in such a way that
Y=Cos(X), and X uniformly distributed in (-?, ?). Determine the mean of Y.
b) The PDF of random variable X is provided by , f(x)=(1/2)e-?x/2?, -?
7. The PDF of Random variable in the range (-3, 3) is provided by,
f(X)= (1/16) (3+X2); -3 ? X ? -1
(1/16)(6-2X2); -1 ? X ? 1
(1/16)(3-X)2; one ? X ? 3
prove that the mean of X is Zero.
8. a) Classify the stochastic process with example.
b) discuss the statistical averages and ensemble averages with examples. provide its significance.
9. describe and provide the significance of subsequent distribution functions. a)Gaussian distribution b) Chi-square distribution c)Poisson distribution d)Binomial distribution e) Uniform distribution.
10. a) The internal noise of a digital receiver has RMS value of 4V.When the signal is applied, the RMS output is 10V. What would be the RMS value of the output, when the signal is halved? The signal and noise are random variables with zero mean.
b)An AM signal is provided by, Xc(t)=AX(t).Cos(?ct + ?),Where X(t) is a zero mean stationary process. It is provided that X(t) and ? are independent. A and ?c are constants and ? is uniformly distributed in (-?,?).Show that Xc(t) is WSS.
11. A random process is provided by X(t) =ACos(?t+?), -? < t < ?.Where A and ? are constants and ? is uniform random variable over(0,2?). Prove that X(t) is WSS.
12. A random process is provided by X(t)=Cos(?t+?), -? < t < ?.Where ? is a constant and ? is uniformly distributed in (0, 2?).Prove that X(t) is Ergodic process.
| Earning: Approval pending. |
