Prob & Stats - Markov Chains (15 of 38) How to Find a Stable 3x3 Matrix

In this video I will find the stable probability and distribution matrix, 3x3 matrix.

Next video in the Markov Chains series:

[dlat]

I can't say thank you enough for this video. I have been fighting with this kind of equation, and I just couldn't understand it, I have been sitting on my desk looking at the example my Teacher gave to me, and lost and waited 3 days. Come to find out she left essential steps out ( which you Sir made sure to explain) assuming I know and completely understand what is going on (online classes), also giving me instructions via email out of the book didn't really cut it. So Sir i have to thank you again for this video because first it showed me there is no comparison to in class lectures also gave me hope to pass my final.

[ikri]

thank you so much for this! My book only gave an example for a 2x2 matrice and I could not find an example for a 3x3 matrice in the book or on the internet until this video!!! It is easier than what I thought it would be, thank you again for your explanations.

[viallykazadimutombo]

You just made it easy to understand. I am more than thankful for this. Thank you

[joeyquiet]

thank you professor for those great videos, I guess i watched too fast, now, I am re-watching some of those videos :)
and, a little python code to do the work,
this works for any dimension Markov matrix.

P = np.array([ # probability matrix
[0.8, 0.2, 0.3],
[0.1, 0.7, 0.1],
[0.1, 0.1, 0.6]
])

rows = len(P)
X = np.zeros(rows)
X[-1] = 1
P = P - np.identity(rows)
P[-1] = np.ones(rows)
print(np.linalg.solve(P, X))

[kudomiezy]

Why didn't you use the third equation to solve the equations? I don't understand actually and confuse a bit about the steady state. If I used Gaussian to solve the equations, I should replace the fourth equations with which row actually?

[mathsLaw]

I really liked your explanations. Pretty simple, easy to follow. Thank you so much.
One question. You have not used the last equation: (0.1A+0.1B+0.6C=C), if the A, B, C you solved does not check with this last equation. Does this mean this Markov Chain does not have any Steady State Matrix ? Thank you

[Hobopower]

Why aren't the rows in the original matrix summing to 1? Is that not necessary?

[everaldasolange]

You are amazing professor, Thanks for sharing this video =D

[indernesgud]

Hi Sir, I just have a couple of questions:
wouldn´t it be easier to solve by gaussain elimination, and can we replace one of the equations with A+B+C = 1 ? In the Gaussian matrix?

Thanks!!

[manjeetsingh]

thanku sir to provide us a video with clear example

[subramanyam]

Very interesting lectures. but you have wasted most of the time doing trivial calculations. Some other ways should have been tried to make it more interesting.