8. Let X be the simple symmetric random walk on the integers in continuous time, so that Pi,i+1 (h) = Pi,i-1 (h)= ah+o(h). Show that the walk is persistent. Let T be the time spent visiting m during an excursion from 0. Find the distribution of T.

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Q: What is the simple random walk on integers? Does it always return to the origin if p = ½ ? if p ≠ ½?

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A: Applying Central Limit Theorem (CLT)..........................

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Q: Find the probability for P(y 3) if y is distributed as N(1, 9)

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