%Andrew McCallum
%Problem Set 11
%Nov. 12, 2007

clc;
clear;
close all;

%Increase the display precision of my variables.
format('long','g');

%1.a.
%Bernoulli draws are Binomial draws where nn = 1
nn = 1;
p = 0.52
%matrix dimensions:

%for question 3bern;
results = 9999*ones(7,4);
for i = 1:1:7;
m = 10^i;
n = 1;
%Bernoulli draws
rand('seed',0);
x = binornd(nn,p,m,n);

%1.b. Closed form MLE for Bernoulli is phat = xbar;
p1b = mean(x)

%1.c.
%There are a few good examples of how to set up a uni- or multivariate
%function without using sperate files at the end of question 1.c. Agrawal 
%and I did the first question from Pset 10 using only inline functions. See the
%file Pset10Q1_inline.m.

%X0 is the initial value for r. Since we aren't minimizing w.r.t. to xbar
%or m we don't need initial values for them.
x0 = 0.1;
xbar = mean(x);
p1c = fminsearch(@(r) lnbernoulike(r,x), x0)

%1.d.
%Solve the FOC. fsolve sets a function equal to zero and solves it w.r.t
%the variable following the @ symbol.

p1d = fsolve(@(r) lnbernoufoc(r,x),x0)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%3.Bernoulli

results(i,1) = i;
results(i,2) =p1b;
results(i,3) =p1c;
results(i,4) =p1d;

end 

% %A short example for how to set up a univariate function without using
% %seperate files:
% sqr = @(x) x.^2 + 3.*x;
% fplot(sqr, [-4,4]);
% xmin = fminsearch(sqr,10);
% %A multivariate example:
% parabl = @(x,y) x.^2 + y.^2;
% [X,Y] = meshgrid(-8:0.5:8);
% Z = parabl(X,Y);
% mesh(X,Y,Z,'EdgeColor','cyan');