GATE EC 2018 Set 1 — Question 50
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Communications → Digital Modulation & Detection → MAP & ML Detection
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Question
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 asthen the value of (accurate to two decimal places) is _______.
Correct answer
-0.5
Solution
Given:
,
for
The MAP rule chooses that maximizes :
For : for
For : for Comparing the two:
,
for
The MAP rule chooses that maximizes :
For : for
For : for Comparing the two:
1.For : Only has a non-zero value (), so .
2.For : Both are non-zero. Since , we choose , so .
3.For : Only has a non-zero value (), so .
The decision boundary where the decision changes from to is at . Thus, .Continue learning with Success Tracker
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