%help stats
%random number generator
seed=931316785;
rand('seed',seed);
randn('seed', seed);

    
% normal probability density function
% mean=0, standard deviation=1
x = [-3:0.1:3];
f = normpdf(x,0,1);
plot(x,f)
title('normal pdf')
pause;

%cumulative probability density function
% for normal pdf with mean=0, standard deviation=1
x = [-3:0.1:3];
p = normcdf(x,0,1);
plot(x,p)
title('normal cumulative df')

pause;


%inverse cumulative distribution function
x = [-3:0.1:3];
xnew = norminv(normcdf(x,0,1),0,1);
%how does xnew compare with x?

p = [0.1:0.1:0.9];
pnew = normcdf(norminv(p,0,1),0,1);
%how does pnew compare with p?

%note that the relationship between a cdf and
%its inverse function is more complicated for
% discrete distributions

%binomial pdf for n=10 and p=1/2 (e.g., how many heads
% for flipping 10 a coin ten times)
x = 0:10;
y = binopdf(x,10,0.5);
plot(x,y,'+')
title('binomial distribution')

pause;

%chi-square distribution
%4 degrees of freedom
x = 0:0.2:70;
y = chi2pdf(x,4);
plot(x,y)
hold on;
%chi-square distribution
%20 degrees of freedom
x = 0:0.2:70;
y = chi2pdf(x,20);
plot(x,y)
title('two chi-2 distributions')
pause;
hold off

%discrete uniform distribution
x = 0:10;
y = unidcdf(x,10);
stairs(x,y)
set(gca,'Xlim',[0 11])
pause;
set(gca,'Xlim','default')
title('discrete uniform distribution')

%exponential pdf

x = 0:0.1:10;
y = exppdf(x,2);
plot(x,y)
title('exponential pdf')
pause;

%F distribution
x = 0:0.01:10;
y = fpdf(x,5,3);
plot(x,y)
title('F distribution')

pause;
%Poisson distribution
x = 0:15;
y = poisspdf(x,5);
plot(x,y,'+')
title('Poisson pdf')

pause;
%student's t-distribution
%versus normal distribution
x = -5:0.1:5;
y = tpdf(x,5);
z = normpdf(x,0,1);
plot(x,y,'-',x,z,'-.')
title('Students t- and normal distributions')