GATE 2019: Communication Quiz 4 (App update required to attempt this test)

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Question 1

A voice band of 300 – 3400 Hz is Nyquist sampled at 8kHz instead of 6.4 kHz
(i) To avoid aliasing
(ii) To make allowance for non sharp cut off filter
(iii) To conserve power
(iv)To conserve bandwidth and enable noise channel to be multiplexed.
The correct statement are

• A(i) and (iii)
• B(ii) and (iv)
• C(i) and (iv)
• DAll of the above

Question 2

Which of the following is true about conditional PDF
A) Conditional PDF is a non-negative function.
B) The area under a conditional PDF is always 1.
C) If the random variables X and Y are statistically independent, then f_Y(y|x) = f_Y(y) and f_X(x|y) = f_X(x).
D) Conditional PDF can be reduced to marginal PDF.

• Aa, b, c
• Bb, c d
• Cc, d, a
• DAll of the above

Question 3

The joint probability density of the random variables X and Y is given by
The probability that X ≤ 1 and Y ≤ 0 is _______.

Answer

Question 4

A baseband binary transmission system sends two pulses S₁(t) and S₂(t) as shown in below figure, through a channel at a rate of 100 kbps to achieve an error probability of 10^-5. If two sided noise PSD is given by 0.510^-7 W/Hz. The required value of magnitude A is


(Assume Q(x)=10^-5for x = 4.27)

• A0.42
• B0.6
• C1.41
• D0.85

Question 5

Let X and Y be two statistically independent random variables uniformly distributed in the ranges (–1, 1) and (–2, 1) respectively. Let Z = X + Y, then the probability that [Z≤-2] is

Answer

Question 6

A system with transfer function H(s) is driven by white noise with power spectral density N₀. The auto correlation of the output signal is measured as the possible transfer function H(s)

• A
• B
• C
• D

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