Hey I'm having trouble in the subject of Markov chains and expected values, would've liked some clarification.
Assuming we have a hyperconnected Markov chain with a transformation matrix P and a stationary distribution π, with X0=x (the initial state). And T is the time between the chain leaving the value x and coming back to it.
I need to A: calculate the expected value E(T) using π(x) and Pxx.B: infer that π(x) <= 1/(2-Pxx).
I have a hard time connecting between distributions and expected values so I'd love your help.