Bernoulli and Markov Length of Run

[kenhung123]

What is the difference between the length of run for both of these sequences and is there any significance?

[/0]

Bernoulli trials are independent of previous trials, Markov trials are conditional on the previous trial

[kenhung123]

Hmm ok but Essentials was trying to prove that in the long run Bernoulli and Markov Chains had different patterns or something which I didn't understand. Is there any distinct pattern that is particularly important?

[vea]

For Markov chains:
In the long run (steady state) the probabilities are unaffected by the first probability (initial state).