A problem in Information Theory: Shannon Entropy equation, Markov Chains

[billtodd]

Homework Statement

I am attaching the problem with the questions in it.

Relevant Equations

Shannon Entropy equation, Markov Chain.

Here is my solution to this problem:
2.1 $\log_2(10,000)\approx 13.2877[bits/sec]$.
2.2 $\log_2(10,000/2)=12.2877[bits/sec]$
2.3 $2\log_2(10,000)\approx 26.575[bits/sec]$
3. For this, I said that $P(Y_n|X_n)=7/8 P(X_n|X_n)+1/8 P(X_n+0.5|X_n)=7/8\cdot 0 +1/8 \cdot 0.5+1/8\cdot 0$, where I think that: $P(X_n|X_n)=0$, I am not sure this is correct. Anyways, I get that: $P(Y_n|X_n)=1/16$, and in order to show that it's Markovian I need to just say that it's $X_n$ w.p. 7/8 and $X_n+0.5$ w.p 1/8. The seuqence $X_n+0.5$ is still Markovian, adding a constant to a Markovian doesn't change the fact that it's Markovian. Is this reasoning correct?
4. My answer was multiplying by 1/16 all of the results in section 2.
5. I am not sure how to answer.
Any hints, and advice on how to answer those questions?

Thanks in advance!