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# GATE 2024 Communication System Foundation Quiz 37

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Question 1

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 2

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

Question 3

Consider a random process x(t) and its derivative . Assume that the derivatives are well defined. The cross correlation function Rxx(t1, t2) is

Question 4

Consider a matched filter which is matched to the following signal s(t).

The output y(t) of the matched filter is maximum at t = …. sec and y(t) value is?

Question 5

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______.
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