GATE Electronics and Communications (EC) 2018 Solved Paper

A binary source generates symbols 𝑋 ∈ {−1, 1} which are transmitted over a noisy channel. The probability of transmitting 𝑋 = 1 is 0.5. Input to the threshold detector is 𝑅 = 𝑋 + 𝑁. The probability density function f_N(𝑛) of the noise 𝑁 is shown below:

If the detection threshold is zero, then the probability of error (correct to two decimal places) is ________.