GATE ECE (Electronics) Test: Random Process Free Online Test 2026
MCQ Practice Test & Solutions: Test: Random Process (20 Questions)
You can prepare effectively for Electronics and Communication Engineering (ECE) GATE ECE (Electronics) Mock Test Series 2027 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Random Process ". These 20 questions have been designed by the experts with the latest curriculum of Electronics and Communication Engineering (ECE) 2026, to help you master the concept.
Test Highlights:
- - Format: Multiple Choice Questions (MCQ)
- - Duration: 60 minutes
- - Number of Questions: 20
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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
as shown in fig.Detailed Solution: Question 1
Consider a low-pass random process with a white-noise power spectral density as shown in fig.
Que: The power PX is
as shown in fig.Detailed Solution: Question 2
If X(t) is a stationary process having a mean value E[X(t)] = 3 and autocorrelation function 
The variance of random variable Y = 
Detailed Solution: Question 3
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: Question 4
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: 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 auto correlation Rxx = (t1 = 0.5T, t2 = 0.7 T) will be
Detailed Solution: Question 6
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: Question 7
The auto correlation function of a stationary ergodic random process is shown in fig.
Que: The mean value E[X(t)] is
Detailed Solution: Question 8
The auto correlation function of a stationary ergodic random process is shown in fig.
Que: The E[X2(t)] is
Detailed Solution: Question 9
The auto correlation function of a stationary ergodic random process is shown in fig.
Que: The variance σx2 is
Detailed Solution: Question 10
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: Question 11
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
If E[X(t)] = 2, the mean value of the system's response Y(t) isDetailed Solution: Question 12
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
where a > 0 is a constant. The cross correlation of X(t) with the output Y(t) is known to have the same form Detailed Solution: 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 average power in Y(t) is
where a > 0 is a constant. The cross correlation of X(t) with the output Y(t) is known to have the same form Detailed Solution: Question 14
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
is applied to a differentiator that has a transfer function H(ω) = j(ω). The output is applied to a network for which Detailed Solution: 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 power spectrum of Y(t) is
is applied to a differentiator that has a transfer function H(ω) = j(ω). The output is applied to a network for which Detailed Solution: Question 16
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 N0 is
Detailed Solution: Question 17
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)
The noise power at the network's output is (F(2) = 0.9773)Detailed Solution: Question 18
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
Detailed Solution: Question 19
A system have the transfer function 
where W is a real positive constant. The noise bandwidth of the system is
where W is a real positive constant. The noise bandwidth of the system isDetailed Solution: Question 20
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