A binary source generates symbols $X\in \left \{ -1,1 \right \}$ 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 $f_{N}\left ( n \right )$ of the noise $\text{N}$ is shown below.
If the detection threshold is zero, then the probability of error (correct to two decimal places) is __________.
