3
5.0 25.0 25.0 05.0 8.0 15.0 025 .0 075 .0 9.0
010
3
16125 .0 37125 .0 4675 .0 07425 .0 56825 .0 3575 .0 04675 .0 17875 .0 7745 .0
010
07425 .0 56825 .0 3575 .0
You simply multiply the position matrix
010 by 3 Pr .
3 Pr , I will demonstrate the matrix
To be more illustrative with the working of
2 Pr :
algorithm in
2
5.0 25.0 25.0 05.0 8.0 15.0 025 .0 075 .0 9.0
For the sum of first row first column:
25.0 025 .0 15.0 075 .09.09.0 . This
th
n )2 ( state, given that on the
means the possibility of having a south wind on
th n state is a south wind.
2 Pr will be the possibility of having a certain
Following the same algorithm,
th n state is a certain
th
n )2 ( state, given that on the
direction of wind on
direction of wind. Thus, if you plug in the position matrix, the possibility
th mn )
(
distribution of each direction of wind on
state will be displayed.
Now our general formula can be concluded:
th mn )
(
On the
day of the voyage, the distribution of the directions of wind
should be
m Pr
Position matrix ×
Shackleton is not really sure about how many days exactly they will reach Antarctica, thus he wants to work out the probability distribution in a very long term, i.e. when total number of days tend to infinity.
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