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, 1] is arcsine-distributed if the cumulative distribution function is given by for all O sx S 1 and the probability density function is given by fx(x) = Given a simple symmetric random walk (S)20 with So -0, we define the folowing random variables: The total number of periods from 0 to 2N the random walk spends above zero: The time of the last visit to 0 before time 2N: The time when the random walk reaches its unique maximum value between time 0 and 2N: M2v argmax(S,:0sn S 2N) (this notation means that Swmax(S, :0s n s 2N). As usual, we start with loading some packages