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Let b > 0 be an integer. Find the probability that a symmetric simple random walk...

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Question

Statistics

Let b > 0 be an integer. Find the probability that asymmetric simple random walk started from 0 visits b the first timein the nth step.

Hint: Draw a picture, and try to describe the requirements thatthe path consisting the first n−1 steps should satisfy. TheReflection principle (or a related result) should be helpful afterthat.

Answer & Explanation Solved by verified expert
3.9 Ratings (507 Votes)
A random walk is symmetric if the probability of going to eachof the neighbors is the sameSince the probability has been asked for visitingb for the first time hence we would firstcalculate the probability of visiting b1 inn1 steps and then multiply it with 12 to get therequired    See Answer
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