The Duke football team can Pass, Run, throw an Interception, or Fumble. Suppose the sequence of outcomes is Markov chain with the following transition matrix. The first play is a pass. (a) What is the...

In the given markov chain, we know that the first play is a pass. So we are at pass initially.
a) Expected number of plays until a fumble or an interception is encountered:
Let this expected number be XP and same expected number from the state R be XR
Then from P we know that there are 3 transitions possible:
The last term in the above equation represents that there is a 0.1 probability that it reaches state
I in 1 step only.
Now we can write similar equation from state R to get:
The last term in the above equation represents that there is a 0.05...