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## A random variable X takes values −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 X̂ = { −1, if Y ≤ θ +1, ifY > θ where the threshold θ ∈ [−1,1] is chosen so as to minimize the probability of error Pr[X̂ ≠ X]. The minimum probability of error, rounded off to 1 decimal place, is ___________.

Asked On2019-07-08 15:39:53 by:KAPILJHADE

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