The following Matlab code was used to investigate the claim that the random number generator randn generates

samples of a ZERO-MEAN random variable. The intent here is to give you an idea of how a specific analysis

might proceed, and to familiarize you with some useful Matlab commands.

% PROGRAM NAME: HW_1

% PURPOSE: To investigate the claim that the randn

% command really does generate a ZERO MEAN random variable

% METHOD: Estimate the 3-sigma range for the estimator

% of the mean using n iid random variables. It should

% become increasingly localized about the true unknown

% mean as n approaches infinity.

% ==============================

xlow=[]; % initialize range limit vector

xhigh=[];

nvec=[];

for i=1:3

n=10^i; % number of iid r.v.s averaged

nvec=[nvec,n];

xmat=randn(n,1000); % generate 1000 realizations of n-vector

xbar=mean(xmat); % compute 1000 measurements of xbar

xlow=[xlow,mean(xbar)-3*std(xbar)]; %essential lower limit of range of xbar

xhigh=[xhigh,mean(xbar)+3*std(xbar)];%essential upper limit of range of xbar

end

plot(log10(nvec),[xlow;xhigh])

xlabel('Base-10 log of number averaged')

title('Estimated 3-sigma range for xbar(n) versus log(n)')