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Highlights from
Chapter 1 Exercises of Introduction to Probability

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Chapter 1 Exercises of Introduction to Probability

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Matlab Implementation of Introductory Probability

HTsimulation.m
%HTsimulation

%Peter wins every time a head turns up

%Peter is in the lead when his winnings are positive.When Peters winnings are 0,...
%he is in the lead if he was ahead at the previous toss

%%
clc;clear all;close all;
tosses=40;
out=rand(tosses,1);
heads=out<0.5;
tails=heads-1;
earnings=[0;cumsum(heads+tails)];
lead=0;
for i=1:tosses
    if earnings(i+1)>0 || (earnings(i+1)==0 && earnings(i)>0)
        lead(i+1)=lead(i)+1;
    else
        lead(i+1)=lead(i);
    end
end

plot(0:tosses,earnings,0:tosses,lead,'r');grid;
xlabel('Number of tosses');legend('Earnings (pennies)','Peter in lead');
title('Peter wins a penny everytime a head turns up and loses one otherwise');
%%

clc;clear all;
tosses=40;
experiments=10000;

out=rand(tosses,experiments);
heads=out<0.5;
tails=heads-1;
earnings=sum(heads+tails);

figure;
hist(earnings,-tosses:2:tosses);grid;
xlabel('Pennies earned');ylabel('Percentage of Occurence');
title('Win Distribution');

%%
%Lead problem
earnings=[zeros(1,experiments); cumsum(heads+tails)];

for i=1:experiments
    lead(i)=0;
   for j=1:tosses
        if earnings(j+1,i)>0 || (earnings(j+1,i)==0 && earnings(j,i)>0)
            lead(i)=lead(i)+1;
        else
            lead(i)=lead(i);
        end
   end
end

figure;
hist(lead,0:2:tosses);grid;
xlabel('No of times in lead');ylabel('Percentage of Occurence');
title('Lead Distribution');

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