GATE EC 2019 Set 1 — Question 57
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Communications → Digital Modulation & Detection → Error Probability
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Question
A random variable takes values and with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise , so that the random variable at the channel output is . The noise is independent of , and is uniformly distributed over the interval . The receiver makes a decisionwhere the threshold is chosen so as to minimize the probability of error . The minimum probability of error, rounded off to 1 decimal place, is ________.
Correct answer
0.1 to 0.1
Solution
Given and . Noise , so for .
The conditional PDFs of are:
for .
for .
The probability of error is:
.
To minimize for , we choose the smallest possible value for , which is .
.
The conditional PDFs of are:
for .
for .
The probability of error is:
.
To minimize for , we choose the smallest possible value for , which is .
.
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