Determine the conditional differential entropy

Question

Solve the following problem:

An additive white Gaussian noise channel has the output Y = X + N, where X is the channel input and N is the noise with probability density function

p(n) = (1/√2πσ_n) e^-n2/2σ2_n

If X is a white Gaussian input with E(X) = 0 and E(X2) = σ2X , determine

1. The conditional differential entropy H(X|N)

2. The mutual information I(X; Y )