Probability modeling : time series probability?

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I am a newbie researcher.

I have a question about probability modeling of time series.

For example, there is a time series such as,

10 8 2 9 1 2 4 6 7 8 9 1 2 3 4 5 6 7...

In above example, I want to express the probability that sample is larger than 8.

Assuming X(n) is time series, or discrete time stochastic process,

"P(X(n) > 8)" seems to be incorrect because X(n) is the set of random variables.

If X(n) is iid process, "P(X(n) > 8)" is correct.

But, How could I express the probability when X(n) is identically distributed but not independent discrete time stochastic process?

If you could help me, I'd appreciate it, really really.