From stochastic independency / to stochastic dependency

[VvvvvVvVBk7]

Hello

my question is the following:
(Please note that english is not my motherlanguage, so kindly ask if i did some explenations that are not understandable i will give my best to correct it)
So I have the following text in front of me and i will translate it to english and afterwords ask my question.


Text:

in a sequence of stochastic independency events x_1, x_2,...

where x_n means its a hit/goal..

i am constructing or making stochastic dependecy events through or out of it with this following knowing.

x_1 x_2 are hits/goals And x_2 x_3 are also hits/goals that means they depend on each other because the average of x_1 x_2 and x_2 x_3 is x_1x_2x_3 and the probability of this average is p^3 and the probability for x_1 x_2 and x_2 x_3 each is p^2.

Now my question:


I got this info in this how the probability works in this dependent stochatsic events but i dont know how it would look in an example of a coin toss with p=0.5 for heads
and heads is a hit/goal?

Could you write me this example?
And also for p=0.33 for heads?


Cause i just started learning depency stochastic and i cant figure out what this example means in a practical example? Does that mean the probability for the events changes and is different if i would have x_1 x_2 x_3 or only x_1 x_2 or only x_2 x_3 ?

i dont underestand what changes so if you could explain me by the given probability p on an example i would be glad

 

[BigBeachBanana]

Can you show the original text, possibly with an example of what you're trying to describe? The language that you used isn't standard. I suspect that by "dependent stochastic model", you meant "Markov Chain".It seems like you have a specific example in mind with the coin toss, but I'm unsure how you define [imath]x_1,x_2,x_3[/imath] nor what you mean by their averages.