Q149
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 as \[ arrayl f_R/0 ( r ) = \ array*20c 1/4,& - 3 r 1\\ 0,& otherwise array .\, and\\ f_R/1 ( r ) = \ array*20c 1/6,& - 1 r 5\\ 0,& otherwise array . array\] The minimum decision error probability is
A source emits bit 0 with probability and bit 1 with probability 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 as
\begin{array}{l} {f_{R/0}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{4},}&{ - 3 \le r \le 1}\\ {0,}&{{\rm{otherwise}}} \end{array}} \right.\,{\rm{and}}\\ {f_{R/1}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{6},}&{ - 1 \le r \le 5}\\ {0,}&{{\rm{otherwise}}} \end{array}} \right. \end{array}
The minimum decision error probability is
\begin{array}{l} {f_{R/0}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{4},}&{ - 3 \le r \le 1}\\ {0,}&{{\rm{otherwise}}} \end{array}} \right.\,{\rm{and}}\\ {f_{R/1}}\left( r \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{6},}&{ - 1 \le r \le 5}\\ {0,}&{{\rm{otherwise}}} \end{array}} \right. \end{array}
The minimum decision error probability is
A.
B.
C.
D.
Answer
Answer: Option D
Solution
Answer: Option D
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