jagguy

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# markov chain sequence

In markov chain you have a transition matrix and initial state.

It is easy to work out the probability on the nth event but what about a sequence of events .

the 1st column .75 is prob a day is wet today given it was wet yesterday .

the 1st column .7 is prob a day is not wet given it was not wet yesterday .

t= .75 .3

.25 .7

what is the probability of a at least 2 days being wet out of the next 3 if it was wet yesterday.

using a markov chain how do i do this?

It is easy to work out the probability on the nth event but what about a sequence of events .

the 1st column .75 is prob a day is wet today given it was wet yesterday .

the 1st column .7 is prob a day is not wet given it was not wet yesterday .

t= .75 .3

.25 .7

what is the probability of a at least 2 days being wet out of the next 3 if it was wet yesterday.

using a markov chain how do i do this?

Start from the state of it was wet yesterday and then work out all the possible final states for the next 3 days (you should have 8 of them). Now find the paths that have 2 or more wet days and add up the probabilities.

P(W|W)*P(W|W)

+

P(D|W)*P(W|D)*P(W|W)

+

P(D|W)*P(W|D)*P(W|W)

This is a three level tree with eight possible outcomes.

You care about four of them.

You care about four of them.

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ASKER

ok so what is the answer and the s0 matrix as it goes along?

You know that we can't just solve the whole problem for you. This is an academic question.

What do you have for it so far?

What do you have for it so far?