# Question regarding Solution 8

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Question regarding Solution 8
Hi,
I just went through the solution for task 8.

First of (Wednesday = 0 )

I found some points rather confusing:

1. We have a primary State M_0 with which we start. This is basically f_0:0.
Because we start at 0 shouldn’t the annotations be always (0:N) because we start from 0?

2. We then do our backward step after we calculated f_1:1 (or f_0:1)
But should we first calculate f_1:2 (f_0:2) so that this backward step makes sense? I thought that backward is just smoothing.

I calculated f_0:2 and then started the backward step.

I got b_2:2 = P (J_2:1|M_2) = P (|M_2) = (1,1,1)^T

After that I got to the backward solution with :

b_1:2 = T * 0_1 * b_2:2

And finally got the probability with:

P(M_1|J_1:2) = α * f_0:1 × b_1:2

The solution calculates with b_2:2 which is the should the state for Friday and not for Thursday if I am not mistaken.

I would be really glad for some feedback.

Best,

Marius Hanisch

I can only give two short answers for now. I’ll look into it more and try to figure out what the logic behind them is.

1. Both the book and the lecture notes use this kind of notation, with 0 denoting the starting time (before we have any evidence). This carries over to f_1:n. What is basically f_0:0 does not use any evidence, so this could be the reason for the notation, while f_1:1 does.

2. Confusingly enough, the smoothing formula and algorithm don’t do exactly the same thing. Let’s fix k to be the time we are interested in. The formula uses f_1:k for the time until k and then b_k+1:n to use the “future” evidence. On the other hand, the Forward-Backward algorithm performs forward updates until time n, and then moves backward.