##### 49. Consider a communication scheme where the ...

49. Consider a communication scheme where the binary valued signal X satisfies P{X = + 1}=0.75 and P{X = -1}= 0.25. The received signal Y = X + Z, where Z is a Gaussian random variable with zero mean and variance σ^{2} . The received signal Y is fed to the threshold detector. The output of the threshold detector \(\hat X\) is:

To achieve a minimum probability of error P{ \(\hat X\) ≠X }, the threshold τ should be

(A) Strictly positive | |

(B) Zero | |

(C) Strictly negative | |

(D) Strictly positive, zero, or strictly negative depending on the nonzero value of 2 σ |

Hint:

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