Question

A drunk man walking simulation
A drunk man stands at origin. There is a cliff at x=10 and home at x=-10. He takes steps randomly left and right. Each step has the probability p of going left and q=1−p of going right.
We desire to simulate and plot 100 random trajectories for the interval of 100 time instants. Once hit at home or cliff, a trajectory is stopped immediately and success or dead is declared. Otherwise, alive is declared. Obtain histograms of [success, dead, alive] for p=0.25, 0.5, and 0.75.

alive = 0
success = 0
dead = 0
p = 0.5
for (n in 1:1000)
{
i = 0
s = 0
while (s < 10 && s > -10 && i < 100)
{
x = rbinom(1, 1, p)
if(x == 1)
s = s-1
else
s = s+1
i = i+1
}
if(s == 0)
alive = alive +1
if(s == 10)
success = success + 1
if(s == -10)
dead = dead + 1
}
barplot(c(success, dead, alive))

this code not working

i need histogram and trajectories and code of mathlab

Answer 1

Note: The plots generated by you maybe different as each time the code is run, different values of probability are calculated at random.

The required code is given below.

    clear;
clc;

p = [0.25 0.5 0.75];
figN = 1;
for k = 1:numel(p)
    alive = 0;
    success = 0;
    dead = 0;
    for n = 1:100
        figure(figN)
        my_title = sprintf('p = %.2f\n',p(k));
        title(my_title)
        hold on
        i = 0;
        s = 0;
        y = 0;
        while (s<10 && s>-10 && i<100)
            x = binornd(1,p(k));

                if x == 1
                    sNew = s - 1;
                    plot([s sNew],[y y+1],'k-')
                    s = sNew;
                else
                    sNew = s + 1;
                    plot([s sNew],[y y+1],'k-')
                    s = sNew;
                end
                i = i + 1;
                y = y + 1;
        end

        if s == 0
            alive = alive + 1;
        elseif s == 10
            success = success + 1;
        elseif s == -10
            dead = dead + 1;
        end
    end
    figure(figN+1)
    my_title = sprintf('p = %.2f\n',p(k));
    labels = {'Success', 'Dead', 'Alive'};
    bar([success, dead, alive])
    title(my_title)
    set(gca,'xticklabel',labels)
    figN = figN+2;
end