Test: Random Process - Electronics and Communication Engineering (ECE) MCQ

Test: Random Process - Electronics and Communication Engineering (ECE) MCQ

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20 Questions MCQ Test GATE ECE (Electronics) Mock Test Series 2025 - Test: Random Process

Test: Random Process for Electronics and Communication Engineering (ECE) 2024 is part of GATE ECE (Electronics) Mock Test Series 2025 preparation. The Test: Random Process questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Random Process MCQs are made for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Random Process below.
Solutions of Test: Random Process questions in English are available as part of our GATE ECE (Electronics) Mock Test Series 2025 for Electronics and Communication Engineering (ECE) & Test: Random Process solutions in Hindi for GATE ECE (Electronics) Mock Test Series 2025 course. Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free. Attempt Test: Random Process | 20 questions in 60 minutes | Mock test for Electronics and Communication Engineering (ECE) preparation | Free important questions MCQ to study GATE ECE (Electronics) Mock Test Series 2025 for Electronics and Communication Engineering (ECE) Exam | Download free PDF with solutions
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Test: Random Process - Question 1

Consider a low-pass random process with a white-noise power spectral density   as shown in fig. ​ ​ ​ Que: The auto correlation function Rx(τ) is

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Test: Random Process - Question 2

Consider a low-pass random process with a white-noise power spectral density   as shown in fig.   Que: The power PX is

Detailed Solution for Test: Random Process - Question 2

Test: Random Process - Question 3

If X(t) is a stationary process having a mean value E[X(t)] = 3 and autocorrelation function  The variance of random variable Y =

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Test: Random Process - Question 4

A random process is defined by X(t) = Acos(πt) where A is a gaussian random variable with zero mean and variance σπ2. The density function of X(0)

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Test: Random Process - Question 5

The two-level semi-random binary process is defined by X(t) = A or -A

where (n-1)T < t < nt and the levels A and -A occur with equal probability. T is a positive constant and

Que: The mean value E[X(t)] is

Detailed Solution for Test: Random Process - Question 5

Test: Random Process - Question 6

The two-level semi-random binary process is defined by X(t) = A or -A

where (n-1)T < t < nt and the levels A and -A occur with equal probability. T is a positive constant and

Que: The auto correlation Rxx = (t1 = 0.5T, t2 = 0.7 T) will be

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Test: Random Process - Question 7

A random process consists of three samples function X(t, s1 ) = 2, X(t, s2 ) = 2cos t1  and X(t, s3 ) = 3sint  - each occurring with equal probability. The process is

Detailed Solution for Test: Random Process - Question 7

The mean value is time dependent so X (t) is not stationary in any sense.

Test: Random Process - Question 8

The auto correlation function of a stationary ergodic random process is shown in fig.

Que: The mean value E[X(t)] is

Detailed Solution for Test: Random Process - Question 8

We know that for ergodic with no periodic component

Test: Random Process - Question 9

The auto correlation function of a stationary ergodic random process is shown in fig.

Que: The E[X2(t)] is

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Test: Random Process - Question 10

The auto correlation function of a stationary ergodic random process is shown in fig.

Que: The variance σx is

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Test: Random Process - Question 11

A stationary zero mean random process X(t) is ergodic has average power of 24 W and has no periodic component. The valid auto correlation function is

Detailed Solution for Test: Random Process - Question 11

For (A) : It has a periodic component.
For (B) ; It is not even in τ, total power is also incorrect.
For (C) It depends on t not even in τ and average power is ∞

Test: Random Process - Question 12

A stationary random process X(t) is applied to the input of a system for which  If E[X(t)] = 2, the mean value of the system's response Y(t) is

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Test: Random Process - Question 13

A random process X(t) is applied to a network with impulse response   where a > 0 is a constant. The cross correlation of X(t) with the output Y(t) is known to have the same form

Que: The auto correlation of Y(t) is

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Test: Random Process - Question 14

A random process X(t) is applied to a network with impulse response   where a > 0 is a constant. The cross correlation of X(t) with the output Y(t) is known to have the same form

Que: The average power in Y(t) is

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Test: Random Process - Question 15

A random noise X(t) having a power spectrum    is applied to a differentiator that has a transfer function H(ω) =  j(ω). The output is applied to a network for which

Que : The average power in X(t) is

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Test: Random Process - Question 16

A random noise X(t) having a power spectrum    is applied to a differentiator that has a transfer function H(ω) =  j(ω). The output is applied to a network for which

Que : The power spectrum of Y(t) is

Detailed Solution for Test: Random Process - Question 16

Test: Random Process - Question 17

White noise with power density N0 /2 is applied to a low pass network for which |H(0)| = 2. It has a noise bandwidth of 2 MHz. If the average output noise power is 0.1 W in a 1 - Ω( resistor, the value of Nis

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Test: Random Process - Question 18

An ideal filter with a mid-band power gain of 8 and bandwidth of 4 rad/s has noise X(t) at its input with power spectrum    The noise power at the network's output is (F(2) = 0.9773)

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Test: Random Process - Question 19

White noise with power density N0 /2 = 6 μW/Hz is applied to an ideal filter of gain 1 and bandwidth W rad/s. If the output's average noise power is 15 watts, the bandwidth W is

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Test: Random Process - Question 20

A system have the transfer function   where W is a real positive constant. The noise bandwidth of the system is

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