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# GATE 2023 Communication System Rank Booster Quiz 35

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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.

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

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______.

Question 7

An LTI system has a wide-sense stationary (WSS) input signal with zero mean. Its output is
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