Please show the work in Python thank you !

Problem 3 (4pt) We repeat the above steps but now for the random variable M2N , the time when the maximum is reached. Write a function that takes a random walk path of length 2N and evaluates the value of M2N on it. 1. Function: timeHitMax (. . . ) Input: . path: Realization of the random walk from the function randomWalk (2N) (Array of length 2N + 1) Output: . result: Realization of the random variable M2N (scalar) In [12]: def timeHitMax ( randomWalk) : ## WRITE YOUR OWN CODE HERE ## HINT: USE numpy . argmax( ) if randomWalk. ndim == 1: result = np. argmax ( randomWalk) if randomWalk. ndim == 2: result = np. argmax ( randomWalk, axis = 1) return result In [6] : ## TEST YOUR FUNCTION HERE path = randomWalk(20) print (path) timeHitMax (path) [0, 1, 2, 1, 0, -1, -2, -1, 0, -1, -2, -3, -4, -5, -6, -7, -6, -7, -8, -9, -8, -9, -10, -9, -8, -7, -8, -7, -6, -5, -6, -5, -4, -5, -4, -3, -2, -3, -4, -5, -4]2. Write a function sampleMaxTime that samples M paths of the random walk, runs timeHitMax on each of them and returns an Array of length M that contains the resulting empirical distribution of M2N . Even more amazingly, it turns out the limiting distribution of Man is again the arcsine distribution, i.e. the histograms of MEN and L2N should look very similar! Run your samp leMaxTime function with N=250 and M=10,000 simulations and plot the histogram of M2N . Modify the plotting code below as needed. As mentioned the shape of the histogram should look like the arcsine density above. [ ] : # COMPLETE/ MODIFY THE PLOT COMMANDS ACCORDINGLY N = 250 M = 10000 c= sampleMaxTime (N, M) # This has to be replaced by the simulated values for M_2N ! ! ! plt . figure (figsize=(10,5) ) pit. title("Normalized histogram for 10000 realisations of $M_{500}$") plt. hist(c, bins='auto', density='True' ) plt . legend ( ) pit . show( )