PROBLEM 2

Python Homework 4: Arcsine Laws The purpose of this python homework is to explore the so-called Arcsine laws numerically. The arcsine laws are a number of fascinating results for random walks. They relate path properties of the simple symmetric random walk to the arcsine distribution. A random variable x on [0, 1j is arcsine-distributed if the cumulative distribution function is given by PIX Farcsin(va) for all 0 sxs 1 and the probability density function is given by on (0,1) Given a simple symmetric random walk (Sn2owith So 0, we define the following random variables: The total number of periods from o to 2N the random walk spends above zero: . .The time of the last visit to o before time 2N The time when the random walk reaches its unique maximum value between time o and 2N M2N:- argmax{Sn: 0