Consider a binary transmission of bits 0 and 1 with equal probability. Bits are transmitted in a noisy channel and channel noise is additive in nature. The received signal is random in nature with conditional probability density function for each transmitted bit 0 and 1, respectively, as
f_r/0(x) = 1 - |x||x| < 1
f_r/0(x) = 1 - |x - 1| 0 < x < 2
What is the average probability of error if threshold in the decision device at the receiving end is 1?

A. $$\frac{1}{3}$$

B. $$\frac{1}{2}$$

C. $$\frac{1}{8}$$

D. $$\frac{1}{4}$$

Answer: Option D