1. Use Bayes' rule to convert the conditioning of event B given event Ai into the conditioning of event Ai given event B for the i= 1, 2, ..., N
2. A discrete memoryless channel is used to transmit binary data. The channel is discrete in that it is designed to handle discrete messages and it is memoryless in that at any instant of time the channel output depends on the channel input only at that time. Owing to the unavoidable presence of noise in the channel, errors are made in the received binary data stream. The channel is symmetric in that the probability of receiving symbol 1 when symbol 0 is sent is the same as the probability of receiving symbol 0 when symbol 1 is sent. The transmitter sends 0s across the channel with probability p0 and 1s with probability p1.
The receiver occasionally makes random decision errors with probability p; that is, when symbol 0 is sent across the channel, the receiver makes a decision in favor of symbol 1, and vice versa. Referring to Figure P3.5, determine the following a posteriori probabilities:
a. The conditional probability of sending symbol A0 given that symbol B0 was received.
b. The conditional probability of sending symbol A1 given that symbol B1 was received.
