RandomWalks

1.  It is late night and a drunkard is walking along a very long street.  The drunkard is not sure which is the way home, so he randomly takes steps of length 1.0 m forward or backward. He takes one step every second continuously for 1 hr.
a. Simulate this process by using a random number generator . Note that  the C Library provides one;  use man srand to learn more about this.
b. Generate 100 different realizations of  the  random sequence of steps by using a different seed each  time. 
c. Graphically show the randomwalks.
d. Calculate the displacement of the drunkard for each realization, and show graphically how these are distributed using a histogram.
e. Calculate the mean and the  root mean square (rms.) displacement of  the drunkard after 1hr.
f. Increase the time (number of steps) and show that the mean displacement  tends to 0 and the rms. displacement scales as the square -root of the time.  Also try to derive the same result analyticaly.