A source emits bit 0 with probability 1/3 and bit 1 with probability 2/3. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are as\({{\rm{f}}_{\left( {{\rm{R}}/0} \right)}}\left( {\rm{x}} \right) = \left\{ {\frac{1}{4}, - 3 \le {\rm{x}} \le 1} \right.{\rm{and\;}}{{\rm{f}}_{\left( {{\rm{R}}/1} \right)}}\left( {\rm{x}} \right) = \left\{ {\frac{1}{6}, - 1 \le {\rm{x}} \le 5} \right.\) The minimum decision error probability is

A source emits bit 0 with probability 1/3 and bit 1 with probability 2

1.	A source emits bit 0 with probability 1/3 and bit 1 with probability 2/3. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are as\({{\rm{f}}_{\left( {{\rm{R}}/0} \right)}}\left( {\rm{x}} \right) = \left\{ {\frac{1}{4}, - 3 \le {\rm{x}} \le 1} \right.{\rm{and\;}}{{\rm{f}}_{\left( {{\rm{R}}/1} \right)}}\left( {\rm{x}} \right) = \left\{ {\frac{1}{6}, - 1 \le {\rm{x}} \le 5} \right.\) The minimum decision error probability is
A.	0
B.	\(\frac{1}{{12}}\)
C.	\(\frac{1}{9}\)
D.	\(\frac{1}{6}\)
Answer» E.

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A source emits bit 0 with probability 1/3 and bit 1 with probability 2/3. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are as\({{\rm{f}}_{\left( {{\rm{R}}/0} \right)}}\left( {\rm{x}} \right) = \left\{ {\frac{1}{4}, - 3 \le {\rm{x}} \le 1} \right.{\rm{and\;}}{{\rm{f}}_{\left( {{\rm{R}}/1} \right)}}\left( {\rm{x}} \right) = \left\{ {\frac{1}{6}, - 1 \le {\rm{x}} \le 5} \right.\) The minimum decision error probability is

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