[Chicago] Anyone know how to do this using Pomegranate?

[Lewit, Douglas]

So let's say we have the following transition matrix:

0.7   0.2   0.1
0.3   0.4   0.3
0.2   0.3   0.5

And let's say we have the following emissions matrix:

0.7   0.2   0.1
0.2   0.6   0.2
0.1   0.1   0.8

The initial state vector is given by 1  0  0.  (So in regular English,
there's a 100% chance of starting in State 1 and 0% chances of starting in
any other state.)

What confuses me is 1) The algorithm for getting to the next state vector,
and 2) Is there a way to do this using the Pomegranate library?  (Probably
is, but not sure what to do)

I know the next state vector is:
0.5185185185     0.4444444444      0.037037037037....

So in regular English there's a 52% chance of being in the first state for
T=2.  (Assuming we start counting at T=1.)   There's a 44% chance of being
in the second state for T=2.  And finally there's about a 4% chance of
being in the third state for T=2.  Can someone tell me where these values
are coming from?  And how can I use Pomegranate (which I installed via
conda) to get these same values?

Much appreciated.

Best,

Douglas.
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