00:01
In this question, it is given a case of markov process.
00:12
So, the given informations are, suppose that it has rained for the past three days, then it will rain today.
00:22
Suppose today is friday and we have to determine for saturday.
00:30
Right.
00:31
So, we, the raining or not raining on saturday depends upon past three days, that is thursday.
00:42
Wednesday, thursday and friday.
00:47
Right.
00:48
Now it is given it will rain today with probability 0 .8 if it has rained for past 3 days.
00:54
Rain, rain, rain, then it will rain with probability 0 .8.
01:02
Next, if we did not rain for any of the past 3 days then it will rain today with probability 0 .2.
01:08
Let us first write what are the possible out.
01:10
Comes for rr n, r nr, nr, nr, r nr nr nr, nr and nr, right? these are the eight possible outcomes.
01:33
Next it is given that if it did not rain for any of the past three days then it will rain today with the probability 0 .2 and it in any other case the weather today will with probability 0 .6 be same as the weather yesterday.
01:48
That is it was raining.
01:51
So this becomes 0 .6, 0 .6, 0 .6, while this becomes 0 .4, 0 .4 and 0 .4.
01:59
Right? now we have to determine the transition probability matrix.
02:07
For this markov chain, so transition probability matrix becomes p is equals to rrrd, rrd, rrn.
02:23
Rnr, n -r -r -r -r -r -n -r -n -r -n -n n -r and n -nn, n -r and n -n, right? similarly, r -r -r -r -n, r -r -n -n, rnr -n -n -r -n -r -n -r -n -r -n -r -n -r -n -r -n -r -n.
03:04
Nnr and nnn...