# Test: Random Process

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

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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) 2023 Mock Test Series for Electronics and Communication Engineering (ECE) Exam | Download free PDF with solutions
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

Solution:  QUESTION: 2

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

Solution: 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 = Solution:  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)

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 mean value E[X(t)] is

Solution: 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

Solution:  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

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

QUESTION: 8

The auto correlation function of a stationary ergodic random process is shown in fig. Que: The mean value E[X(t)] is

Solution:

We know that for ergodic with no periodic component QUESTION: 9

The auto correlation function of a stationary ergodic random process is shown in fig. Que: The E[X2(t)] is

Solution: QUESTION: 10

The auto correlation function of a stationary ergodic random process is shown in fig. Que: The variance σx is

Solution: 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

Solution:

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 ∞

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

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 auto correlation of Y(t) is

Solution:  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

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 average power in X(t) is

Solution: 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

Solution:  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

Solution:  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)

Solution:  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

Solution:   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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