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Electronics and Communication Engineering

GATE ECE Random processes PYQs

Build your understanding with focused practice from past exam papers.

Questions 11–14 of 14. Imported answers require independent review unless marked reviewed.

Topic practice 14 questionsPage 2 of 2

Question 28

Open question
ECMCQ2 marksNeeds review
Consider a white Gaussian noise process

with two-sided power spectral density

W/Hz as input to a filter with impulse response

(where t is in seconds) resulting in output Y(t). The power in Y(t) in watts is
Your answerChoose one option.

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Question 40

Open question
ECNAT2 marksNeeds review
A random variable

takes values

and

with probabilities

and

, respectively. The noisy observation of

is

, where

has uniform probability density over the interval

.

and

are independent. If the MAP rule based detector outputs

as

then the value of

(accurate to two decimal places) is ______.

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Question 22

Open question
ECNAT1 markNeeds review
Consider the random process

where

is a zero-mean Gaussian random variable and

is a random variable uniformly distributed between 0 and 2. Assume that

and

are statistically independent. The mean value of the random process at

is __________

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Question 51

Open question
ECMCQ2 marksNeeds review
Let

be a wide sense stationary random process with the power spectral density

as shown in Figure (a), where

is in Hertz (Hz).
Diagram for Electronics and Communication Engineering question 51

The random process

is input to an ideal lowpass filter with the frequency response

as shown in Figure (b).
Diagram for Electronics and Communication Engineering question 51 (figure 2)

The output of the lowpass filter is

.
Let

be the expectation operator and consider the following statements:
I.

II.

III.

Select the correct option:
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