Question

Help! Linear algebra!
If, on the first observation the system is in state 1, what is the probability that it is in state 1 on the third observation?

Answer 1

\[\left[\begin{matrix}.6 & .4 \\ .7 & .3\end{matrix}\right]\]Is the Markov Chain transition matrix.
Not sure what this is asking.

Answer 2

you need to do some matrix multiplication

Answer 3

What am I multiplying? I'm new with this, so I'm a bit lost.

Answer 4

\[\left[\begin{matrix}1 & 0 \end{matrix}\right]\left[\begin{matrix}.6 & .4 \\ .7 & .3\end{matrix}\right]^2\]

Answer 5

That worked! We aren't allowed to use calculators, though so it would take a bit of time to do it this way. Is there a way to do it with a probability tree?

Answer 6

.6*.6+.4*.7

Answer 7

so yes

Answer 8

What if it said it was in the second state and to find the probability on the 3rd observation?

Answer 9

so on the first observation start in the second state...what is the prob that on the 3rd observation you are in state 1?

Answer 10

The second state is .4, but I'm not sure what to do after that. Could you draw out the tree really quickly so I could see how you set up the tree? That would help a lot!

Answer 11

did I phrase the question correctly?

Answer 12

or are you still looking at the first question

Answer 13

Shouldn't it say you are in state 1 and what is the prob. that you are in the 3rd observation?

Answer 14

so \(.6\times.6+.4\times.7\)

Answer 15

1->1->1 which is .6*.6

or 1->2->1 which is .4*.7

Answer 16

Thanks! How would it look if the question asked:
on the first observation, the system is in state 2, what state is the system most likely to occupy on the third observation?

I'm not trying to get you to do my homework, I have a bunch of these types of problems I just need to see how to do one

Answer 17

\[\left[\begin{matrix}0 & 1 \end{matrix}\right]\left[\begin{matrix}.6 & .4 \\ .7 & .3\end{matrix}\right]^2\]

then pick the larger of the two


or make a tree