Practice & homework 4

[Yfke]

I've put up the practice & (partial) homework for week 4. I cannot access surfdrive right now (maintenance) so will do the rest of homework 4 next week. Assigning this issue to myself.

@cschaffner I checked the exercises on stochastic processed and they are not super hard, but for a practice session where the students are new to the topic I think they will be challenging enough. A quick overview for you before the werkcollege:

4(a) is pretty straightforward (compute entropy rate of i.i.d. bernoulli(p) samples, the answer is h(p)), 4(b) is the observation that this process has the same rate because there is a bijection between the two processes.

5 is that prove/disprove exercise. (a), (c) and (d) are true and are relatively straightforward to prove (applying the definition of stationary process and then maybe one or two steps before/after that). (b) is not true: it has a counterexample of X_1 through X_n being independent fair coin flips, and X_{n+i} = X_{i} from there. This process is stationary but H(X_n|X_0) = 0 < 1 = H(X_{n-1}|X_0).

6 is not a stationary process, but does converge to one (it is a finite-state, aperiodic and irreducible Markov chain*). Maybe we should split it up into two subexercises, first asking the students to draw transition graph and verify that it is aperiodic etc.

7 does not exist yet but I might want to add a starred exercise (suggestions are welcome). Or if I'm missing some of the lecture material please let me know.

*CT says that those chains become stationary as n goes to infinity. This seems intuitive if you draw a few diagrams but a proof is not given and I don't see where to start. If we can figure it out it might be an insightful exercise for the homework or exam?

[cschaffner]

@Yfke I can't find the exercises... did you forget to push?

[Yfke]

Hmm yeah that is very possible :( I'm not home right now & will only have
access to my laptop tomorrow evening when I'm back. Will push then!

On Nov 19, 2016 2:38 PM, "cschaffner" [email protected] wrote:

@Yfke https://github.com/Yfke I can't find the exercises... did you
forget to push?

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[Yfke]

It's online now, sorry about that!

I see that you also saw the poll that I created. It's set to become visible this Tuesday (so we can mention it during the lecture or exercise session), is that ok?

[cschaffner]

Yes, I've added a question about work load and already made it available, I can mention it on Tuesday.
Thanks for the exercises, I'll have a look tomorrow. I was looking through the chapter in CT a bit and I think it would be useful to have as first practice exercise the proof of Thm 4.2.3 about the Cesaro mean, it's a simple little exercise in analysis.

[Yfke]

Added that one too!

[cschaffner]

could you have a look at the concept quiz?

[Yfke]

Done!

When I was looking at question 2, the answer "Flip two random bits b0 and b1 and store them in your 2-bit memory. In every even time step, output b0; in every odd time step, output b1." changed after I clicked it (before, it was output the pair (b0;b1), I think). Did you change that one like 10 minutes ago?

[Yfke]

Ah I see you are still working on it, there was a new question added.

The new question (no. 3) is quite a lot of computation / work for a concept quiz, especially if the student is new to the concept (which most students are). I think it is fine to leave it in, but there are certainly enough questions now. ;) Also, is the choice of which is mu_1 and which is mu_2 standard? Otherwise, it seems that both the current correct answer and the one with mu1/mu2 interchanged are correct, as the only different is the seemingly arbitrary labeling.

[cschaffner]

That's right, but it's exactly done in CT, Example 4.1.1. I gave the states names now, so that is what the 1 and 2 are referring to.

[Yfke]

Ok perfect!

On Nov 21, 2016 21:36, "cschaffner" [email protected] wrote:

That's right, but it's exactly done in CT, Example 4.1.1. I gave the
states names now, so that is what the 1 and 2 are referring to.

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