Test: Random Process


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20 Questions MCQ Test GATE ECE (Electronics) 2023 Mock Test Series | Test: Random Process

Test: Random Process for Electronics and Communication Engineering (ECE) 2022 is part of GATE ECE (Electronics) 2023 Mock Test Series 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) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Random Process below.
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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

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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)

Detailed Solution for Test: Random Process - Question 4

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

Detailed Solution for Test: Random Process - Question 6

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 

Detailed Solution for Test: Random Process - Question 10

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

Detailed Solution for Test: Random Process - Question 13

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

Detailed Solution for Test: Random Process - Question 14

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

Detailed Solution for Test: Random Process - Question 15

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

Detailed Solution for Test: Random Process - Question 17

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)

Detailed Solution for Test: Random Process - Question 18

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

Detailed Solution for Test: Random Process - Question 20

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