Markov Chain in Shackleton’s Voyage
----- Andy Zhang (Y12)
Ernest Shackleton was at South Georgia, preparing for his last journey toward the Antarctica. He attempts to estimate the number of days it might take to get to the Antarctica, by calculating the distribution of different directions of wind (south, north, east or west) every day. With some help from a few statisticians and mathematicians, the directions of wind follows some underlying rules:
After a day of S wind, the probability of getting S on the next day is 0.9,
N is 0.075, EW is 0.025
After a day of N wind, the probability of getting N on the next day is
0.8, S is 0.15, EW is 0.05
After a day of EW wind, the probability of getting EW on the next day
is 0.5, N is 0.25, S is 0.25
Most importantly, the conditional probability of the future and past
states are independent, given the present state. This means that the states before 1 n states are not relevant to this conditional probability.
Here is an illustrative graph,showing the conditional probability
between each state.
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