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.