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S2018-CT4 Q6 part iv)

A

Actuary@22

Very Active Member
Hello
In part iv),as per my understanding third jump is in state C would mean calculating P^4 and looking at the 1st row and 3rd column entry.
But the solution states that we need to calculate P^3.
Please explain how P^3 instead of P^4 is the solution.
 
Hello

At time 0 the process is in State A. Part (iv) is about where the third jump goes, ie at time 3. This is three transitions or jumps:

The first jump is when we go from the state we were in at time 0 (state A) to the state we occupy at time 1
The second jump is when we go from the state we were in at time 1 to the state we occupy at time 2
The third jump is when we go from the state we were in at time 2 to the state we occupy at time 3

As we are dealing with three jumps or transitions, P^3 is the relevant probability transition matrix.

Hope this helps

Andy
 
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