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Bits $1$ and $0$ are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below.

The optimum threshold to achieve minimum bit error rate $(BER)$ is

  1. $\frac{1}{2} \\$
  2. $\frac{4}{5} \\$
  3. $1\\$
  4. $\frac{3}{2} $
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