Given a simple symmetric random walk ()0(Sn)n0 with 0=0S0=0, we define the following random variables:

• The total number of periods from 00 to 22N the random walk spends above zero:

2:=|{{1,,2}:>0}|.C2N:=|{n{1,,2N}:Sn>0}|.

• The time of the last visit to 00 before time 22N:

2:=max{02:=0}.L2N:=max{0n2N:Sn=0}.

• The time when the random walk reaches its unique maximum value between time 00 and 22N:

2:=argmax{:02}(this notation means that 2=max{:02}.

Problem 2 (6 points) Write three Python functions which take a path of a random walk as an input and then compute the values of the random variables C2n, L2N, M2n, respectively, as defined above: ]: ### Insert your code here for total time spend above zero def timeAboveZero (path): ## Write your own code here return result ]: ### Insert your code here for last time the random walk visited zero def TimeofLastvisitofZero (path): ## Write your own code here return result ]: ### Insert your code here for the time when the random walk hits its maximum def timeHitMax(randomWalk): ## Write your own code here return result