Transition matrices - HELP

[nbalakers24]

Hi i'm having trouble with questions 3 and 4.
for question for i cant figure out the inital state matrix.

help appreciated, thanks!

[pooshwaltzer]

Pr(spin|med) = 0.56 = Pr(spin&med)/Pr(spin) --> Pr(spin) = Pr(spin&med)/0.56 ... 1

Pr(med|spin) = 0.70 = Pr(spin&med)/Pr(med) --> Pr(med) = Pr(spin&med)/0.70 ... 2

Pr(med|med) = 0.30 = Pr(med&med)/Pr(med) --> Pr(med) = Pr(med&med)/0.30 ... 3

Pr(spin|spin) = 0.10 = Pr(spin&spin)/Pr(spin) --> Pr(spin) = Pr(spin&spin)/0.10 ... 4

Letting 1 = 4
Pr(spin&med)/0.56 = Pr(spin&spin)/0.10 --> Pr(spin&med) = [0.56*Pr(spin&spin)]/0.10 ... 5

Letting 2 = 3
Pr(spin&med)/0.70 = Pr(med&med)/0.30 --> Pr(spin&med) = [0.70*Pr(med&med)]/0.30 ... 6

Letting 5 = 6
[0.56*Pr(spin&spin)]/0.10 = [0.70*Pr(med&med)]/0.30
[Pr(spin)^2] = (35/84)[Pr(med)^2]
Pr(spin) = [(35/84)^0.5]Pr(med)


Pr(fast|[spin/med]) = 0.50 = Pr(fast&[spin/med])/Pr(fast)
= Pr{(fast)|[Pr(spin) + Pr(med) - Pr(spin&med)]}/Pr(fast)
= Pr{(fast)|[(35/84)^0.5Pr(med) + Pr(med) - 0.70Pr(med)]}/Pr(fast)
= Pr{(fast)|[0.9455Pr(med)]}/Pr(fast)

[aznanthony]

For question 3
A is the transition matrix so to get state matrix after 5 periods calculate A^5*B

[_avO]

Actually A is not the transition, its columns do not equal 1.00

I don't know how to approach this

[nbalakers24]

pooshwaltzer can you use matrices? :S

yeah thats the problem, dont know what to do :S LOL

[aznanthony]

I didn't realise, do you have answers?

[nbalakers24]

question 3 is

93
139
152
41
464

in a 5x1 matrix, i get the same answer but in a 4x1 matrix without the 464. dont know where the 464 comes from