GATE 2023 Communication System Quiz 35

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

S1: 0 ≤ F_x(x) ≤ 1

S2: F_x(x) is a non decreasing function

S3: F_x(–x) = 1 – F_x(x)

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 ____?

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)

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

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

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

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