Solve the following problem:
Channels 1, 2, and 3 are shown in Figure .
1. Find the capacity of channel 1. What input distribution achieves capacity?
2. Find the capacity of channel 2. What input distribution achieves capacity?
3. Let C denote the capacity of the third channel and C1 and C2 represent the capacities of the first and second channels. Which of the following relations holds true and why?
C≤ 1/2(C1 + C2)
C = 1/2(C1 + C2)
C≥ 1/2(C1 + C2)