% binomial.m
% This MATLAB code simulates a binomial distribution
% You are prompted to supply
% the number of tosses to make, the number of 
% simulations to run, and the probability of a head.
%
% The output will be vector: x contains the number of 
% heads on each toss. A histogram for x is plotted
% along with the mean and standard deviation for both
% the vector x and the theoretical mean and variance for 
% the binomial.
!c:
n=input('how many tosses to make:    ')
p=input('probability of a head:     ')
m=input('how many simulations to run:     ')
kj=0;
kheads=0;
ktails=0;
for j=1:m
for i=1:n
a=rand(1,1);
if a <= p
   kheads=kheads+1;
else
   ktails=ktails+1;
end;
end;
x(j)=kheads;
kheads=0;
end;
xbar=mean(x);
stan=std(x);
disp('mean and standard deviation are')
xbar,stan,pause
a=n*p;
b=sqrt(a*(1-p));
disp('np and sqrt(np(1-p)) are')
a,b,pause
hist(x)
title('histogram for m tosses'),pause