HW6-3 Most difficult question

I found this the most difficult question .. and really did way too much research to come up with no good answer. I understand P(A0) and P(B0), the initial states. But I have real trouble with X0 or Y0. Seems to me they don't exist. First time we see an observation is at time1. Then we see the next at t2. All the literature on HMM talks about the 3 major problems (evaluation, decoding, and learning). The really neat AIMA HMM python code example looks at decoding and runs real well, as does even a little online HMM calculator. But the question just asked for some intermediate/arbitrary probabilities. Section 15.3.1 in the textbook shows how to go from t-1 to t going forward and how to set up the T and O matricies, but nowhere is any mention of observations at time=0.

Also I began to see this problem as essentially a coin flip, heads or tails, with a faulty observer who saw Head (when Head was there) 10% of the time and saw Head (when Tail was there) 80% of the time. So is there ONE state variable here, with 2 values, or 2 state variables? Are there really two observations X and Y? (Independent or different ones?) Or is there only one observation with a probablity of being true or false (dependent on the state.) Wasn't sure about that either.

How something so simple can become so confusing ...