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GATE EC 2022: Communication System Quiz 4
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Question 1
The probability density function of a random variable x is shown in figure below
If another random variable Y = 2X, then PDF for Y will be,
Question 2
The PDF of a random variable is fx(x) = ke–bx for x > 0
= 0 for x < 0, and k, b > a
Then k = bP, what is value of P?
Question 3
Consider an LTI system with impulse response given as
. A wide-sense stationary (WSS) random process
with autocorrelation function
, is applied to the input of the above-mentioned system. Find the autocorrelation of the output signal
if its given that ‘A’ and ‘a’ are real positive constants.
![](https://gradeup-question-images.grdp.co/liveData/PROJ17152/1530185373184316.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ17152/1530185373972364.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ17152/1530185374734829.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ17152/1530185375499115.png)
Question 4
For a random process X(t), if the mean is given by 2 and the auto-correlation function is
Rxx(t1,t2)= 5 + 2e-0.1|t1-t2|
Then, the covariance between X(5) and X(2) is _________.
Question 5
A binary baseband digital communication system employs the signal
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be
![](https://gradeup-question-images.grdp.co/liveData/PROJ5662/1498131935313849.png)
for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be
Question 6
A random binary wave y(t) is given by
Where p(t) = u(t) – u(t –T), u(t) is the unit function and f is an independent random variable with uniform distribution in [0, T]. The sequence {Xn} consists of independent and identically distributed binary valued random variables with P{Xn = +1} = P{Xn = –1} = 0.5 for each n.
The value of autocorrelation
equals______.
![Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-3_files\image236.png](https://gs-question-images.grdp.co/1458192448097791.png)
Where p(t) = u(t) – u(t –T), u(t) is the unit function and f is an independent random variable with uniform distribution in [0, T]. The sequence {Xn} consists of independent and identically distributed binary valued random variables with P{Xn = +1} = P{Xn = –1} = 0.5 for each n.
The value of autocorrelation
![Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE EC 10-Mar\GATE-ECE-2015-Paper-3_files\image237.png](https://gs-question-images.grdp.co/1458192448775564.png)
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Jan 20ESE & GATE EC