A digital communications system consists of a transmitter and a receiver. During each short transmission interval the transmitter sends a signal which is interpreted as a zero, or it sends a different signal which is to be interpreted as a one. At the end of each interval, the receiver makes its best guess at what is transmitted. Consider the events:

\(T_0 = \{\mbox{Transmitter sends } 0\}, \quad T_1 = \{\mbox{Transmitter sends } 1\} \)

\(R_0 = \{\mbox{Receiver perceives } 0\}, \quad R_1 = \{\mbox{Reviver perceives } 1\} \)

Assume that \(\mathbf{P}(R_0 \mid T_0)=.99\), \(\mathbf{P}(R_1 \mid T_1)=.98\) and \(\mathbf{P}(T_1)=.5\).

- Compute probability of transmission error given \(R_1\).
- Compute the overall probability of a transmission error.
- Repeat a) and b) for \(\mathbf{P}(T_1)=.8\).

[Pitman page 54, problem 4]