Question

Please help! Linear algebra! Picture attached

Answer 1

Just to make sure I know how to do part a and b... The state vector for time t=2 is just p0*T^2, right? It gives a row vector.

Not sure about part c and d though

Answer 2

@Zarkon @amistre64 @eseidl @TuringTest

Answer 3

Not quite here yet in my Linear Algebra studies, sorry

Answer 4

i remember something about the markov being a condition that reaches an equilibrium after so many iterations .... but i just aint got the time at the moment to review it again. Ill have more time in about 2 hours hopefully if noone else has hit it up

Answer 5

T P_{n-1} = Pn is what im vaguely remembering, which means its most likely in error :)

Answer 6

What's an error?

Answer 7

.... most likely my memory without reviewing the subject matter

Answer 8

\[T~P_o=P_1\]
\[\left[\begin{matrix}.3&.4&.3 \\ .5&.0&.5\\.5&.5&.0\end{matrix}\right]\left[\begin{matrix}.2\\.3\\.5\end{matrix}\right]=P_1\]
\[.06+.08+.06=.2\]\[.15+.00+.15=.3\]\[.25+.25+.00=.5\]
so P1 = [ .2 .3 .5 ]

\[T~P_1=P_2\]

Answer 9

Probability that B does not occur means: P(-B) = 1 - P(B)

Answer 10

http://www.math.ucdavis.edu/~daddel/linear_algebra_appl/Applications/MarkovChain/MarkovChain_9_18/node1.html

and yes, it looks like the recursive setsup the

\[P_n=T^nP_0\]

Answer 11

Ok, so for D...
the probability that the state at time t=2 is NOT B is .71 I found and the probability at time t=1 was B is .35, so to find the probability for that state at time t=2 is NOT B while state at time t=1 was B would be???

Would it just be .35*.71??

Answer 12

im thinking its, P1(B) * P2(-B)

Answer 13

Thanks!