# For the symmetric random walk starting at 0: (a) What is the expected time to return to

## Question:

For the symmetric random walk starting at 0:

**(a)** What is the expected time to return to 0?

**(b)** Let N, denote the number of returns by time n. Show that E[N2] = (2n+1) D) (2") ()" - 1 2n 1.

**(c)** Use

**(b)** and Stirling's approximation to show that for n large E[N] is proportional to Vn.

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