Information and Coding theory. Good answers will be upvoted.

Assume that you have three parallel Gaussian channels with inputs X1, X2, X3 and noises Z1,Z2, Z3, respectively. Assume that the noise powers are E[Z1] 0.4, E[Z21 0.8 and E[Z1] 1.4, while the total available power is 1. Find the optimal power allocation (waterfilling) and corresponding capacity Assume that you have three parallel Gaussian channels with inputs X1, X2, X3 and noises Z1,Z2, Z3, respectively. Assume that the noise powers are E[Z1] 0.4, E[Z21 0.8 and E[Z1] 1.4, while the total available power is 1. Find the optimal power allocation (waterfilling) and corresponding capacity