What input distribution achieves capacity

Question

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)