%% Normal density function
%% Plots of the normal density function
% The MATLAB function *normpdf* gives the normal probability density
% function. If X is a vector then the command *normpdf(X,mu,sigma)*
% computes the normal density with parameters mu and sigma at each value of
% X. The command *normpdf(X)* computes the standard normal density at each
% value of X.
X = [-5:0.01:5];
%% Standard normal density
plot(X,normpdf(X))
%%
% The plot shows a bell shaped curve. 
%% mu=1,sigma=1
plot(X,normpdf(X,1,1))
%%
% We see the point where the graph peaks has shifted.
%% mu=0, sigma=2
% We plot this in red along with the standard normal in blue.
plot(X,normpdf(X))
hold on
plot(X,normpdf(X,0,2),'Color','r')
hold off
%%
% The plot is more spread out and has a lower peak with larger sigma.
%% mu=0, sigma = 1/2
% We plot this in green along with the standard normal in blue
plot(X,normpdf(X))
hold on
plot(X,normpdf(X,0,1/2),'Color','g')
hold off
%%
% The plot is more concentrated near x=0 and the peak is higher.
%% Binomial distribution
% Here are some plots we looked at when we did the binomial distribution,
% first with p=1/2, n=100, then with p=1/3, n=100.
binomplot(100,1/2)
%%
% Notice the resemblance to a normal density.
%%
binomplot(100,0.3)
%%
% Again, notice the resemblance to a normal density.  
%% Cumulative distribution function
% The MATLAB command *normcdf(X,mu,sigma)* gives the cumulative
% distribution function of the normal density with parameters mu, sigma.
% The command *normcdf(X)* gives the cumulative distribution function of
% the standard normal density.
%% Standard normal cumulative distribution function
X = -4:0.01:4;
plot(X,normcdf(X))
%% mu=1,sigma=1
plot(X,normcdf(X,1,1))
%%
% Changing mu translates it.
%% mu=0, sigma=2
plot(X,normcdf(X,0,2),'Color','r')
%%
% With larger sigma it approaches 1 more slowly.
%% mu=0, sigma=1/2
plot(X,normcdf(X,0,1/2),'Color','g')
% With smaller sigma it approaches more rapidly.