First of all, the person in question is a free point and moves in any direction. Secondly, after the drunk leaves his post, because his actions are arbitrary, his chances of returning to his post are almost zero. Because the pillar is not a special position in every position of the drinker's movement, the chances of the drinker returning to any point after starting are the same. So the pillar is not the most likely location.
In fact, this problem can be compiled into a simple MATLAB program to simulate this process:
%%-drunk-%%
clear
plot(0，0，' * ')； Mark pole position with "%".※.
s = 0； ?
S = zero (1,100); ?
%% Suppose there are 1000 drunkards.
For what? j= 1: 1000
n = 100；
%% Generate random numbers for backup.
I = rand (1, n);
J = rand (1, n);
P=[0？ 0]; ? %%P is the position of drunkard.
%% Start walking. . . Assume that the number of walking steps of each drunk is 0 ~ 9; The length of each step is 1.
For what? i= 1:N
P( 1)= P( 1)+fix( 10 * I(I))* cos(J(I)* 2 * pi)； ? %%? Fix( 10*I(i)) is the number of steps (0 ~ 9); J(i)*2*pi？ For the angle
P(2)= P(2)+fix( 10 * I(I))* sin(J(I)* 2 * pi)； ?
%%plot(P( 1)，P(2)，'.'); %% the position of each walk
end
Axis? equal
Keep? exist
%%plot(P( 1)，P(2)，'.'); %% The position of each drunk after 100 lap
s(j)=sqrt((p( 1))^2+(p(2))^2)； ? %% Distance from the last position to the pole
S = S+S(j)； The sum of the final distances of all drunks.
end
hist(s，40)； ? %% statistical distance distribution
e = S/ 1000； ? %% average distance
The result is shown in the figure.
In fact, for all 1000 drunks, the final distance average result is about 50 steps. Because the average number of steps for each drunk is 5, the most likely position is 10 times the average distance each time. Judging from the columnar distribution map, the drunkards with a final distance of about 50 are the most.