Question: For each integer a 1, let Ta = inf{n 0 : Xn = a}. Show that Ta is a stopping time. Define a

For each integer a ≥ 1, let Ta = inf{n ≥ 0 : Xn = a}. Show that Ta is a stopping time.

Define a random variable Yn by the rule Yn =

(

Xn if n < Ta, 2a − Xn if n ≥ Ta.

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