GATE 2019 Electronics & Communication Q47

Question

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 X = {-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 ≠ X]. The minimum probability of error, rounded off to 1 decimal place, is ________.