A digital communications system consists of a transmitter and a reciever. During each short transmission interval the transmitter sends a signal which is to be interpreted as a 0, or it sends a different signal which is to be interpreted as a 1. At the end of each interval, the receiver makes its best guess at what was transmitted. Consider the events: T0= Transmitter sends 0
R0= Receiver concludes that a 0 was sent
T1= Transmitter sends 1
R1= Receiver concludes that a 1 was sent
Assume that P(R0 | T0)= 0.99, P(R1 | T1)= 0.98 and P(T1)= 0.5.
(a) Find the probability of a transmission error given R1.
(b) Find the overall probability of making a transmission error.
(c) Repeat a, b for P(T1)=0.8 instead of 0.5