θ . Where the threshold θ ∈[-1,1] is chosen so as to minimize the probability of error Pr[{X}↖{∧} ≠ X] . The minimum probability of error, rounded off to 1 decimal place, is ______________.">

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GATE Electronics and Communications (EC) 2019 Solved Paper

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Question : 39 of 65

Marks: +1, -0

A random variable X takes −1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the channel output is Y=X+N. The noise n is independent of X, and is uniformly distributed over the interval [−2,2]. The receiver makes a decision

−1	‌	‌ if ‌Y≤θ
+1	‌	‌ if ‌Y>θ.

Where the threshold θ∈[−1,1] is chosen so as to minimize the probability of error Pr[

≠X]. The minimum probability of error, rounded off to 1 decimal place, is ______________.

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