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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 __________.

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