A binary source generates symbols ๐‘‹ โˆˆ {โˆ’1,1} which are transmitted over a noisy channel

Q. A binary source generates symbols ๐‘‹ โˆˆ {โˆ’1,1} which are transmitted over a noisy channel. The probability of transmitting ๐‘‹ = 1 is 0.5. Input to the threshold detector is ๐‘… = ๐‘‹ + ๐‘. The probability density function ๐‘“๐‘(๐‘›) of the noise ๐‘ is shown below.

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

Ans: 0.12 โ€“ 0.14

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