Suppose that whether or not it rains today depends on previousweather conditions through the last two days.

Specifically, suppose that if it has rained for the past twodays, then it will rain tomorrow with probability 0.7; if itrained

today but not yesterday, then it will rain tomorrow withprobability 0.5; if it rained yesterday but not today, then itwill

rain tomorrow with probability 0.4; if it has not rained inthe past two days, then it will

rain tomorrow with probability 0.2. If we let the state attime n depend only on whether or not it is raining at time n,

Q1. ---whether the preceding model is a Markov chain or not?And why? .

And we can transform this model into a Markov chain by sayingthat the state at any time is determined by the weather

conditions during both that day and the previous day. In otherwords, we can say that the process is in

state0 if it rained both today and yesterday,

state1 if it rained today but not yesterday,

state2 if it rained yesterday but not today,

state3 if it did not rain either yesterday or today.

Q2.---The preceding would then represent a four-state Markovchain having a transition probability matrix

P, and find P, plz?

Q3. ---Given that it rained on Monday and Tuesday, what is theprobability that it will rain on Thursday?