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# GATE 2023 Communication System Quiz 35

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Question 1

Read the following statements regarding commutative distribution function (CDF) of a random variable X defined as Fx(x).

S1: 0 ≤ Fx(x) ≤ 1

S2: Fx(x) is a non decreasing function

S3: Fx(–x) = 1 – Fx(x)

Question 2

With input X and output Y in a communication system, the joint probability mass functions of X & Y are listed below. Then P (y =-1 / x = -1) is ____?

Question 3

A noisy channel probability has per digit error probability of 0.01, then the probability of finding more than 1 error if 10 bits are received is___(rounded to 3 decimal)

Question 4

If x(t) is WSS, then what is ?

Where Rxx ( ) is autocorrelation of x(t).

Question 5

Let C1 be the capacity of given Binary Erasure channel and Let C2 be the capacity of given Binary symmetric channel. Assume p = 0.4 then find C1 : C2

Question 6

Consider a baseband random process having an auto correlation function . This process is passed through an ideal differentiator. If the output random process is , its auto correlation function is given by
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