, 08.11.2019 01:31 lovelyheart5337

# Generation of pseudo-random normal rvs. generate sample size of l rvs, each iid n(mu, sigma^2) rvs. histogram these with nbins =25; see myhistc. m under files, or use your own. however, read the next section because an overlay is required. develop a plot where you overlay the normalized histogram (with area 1) with the theoretical pdf. show the goodness of fit is good using a chi-squared test. you should know this from your earlier stats class. take mu=-6, sigma^2 = 2; try different sample sizes of l = 10^2,10^3,10^4. since these are generated using randn, the fit will be excellent and the chi-squared will be small. myhistc. m function [xknt, outknt, xcenter, xdelta] = myhistc(x, nbins, xend); %function [xknt, outknt, xcenter, xdelta] = myhistc(x, nbins, xend); % a histogram with nbins within the range [xend(1), xend(2)] % xend (1: 2), for edges, beyond xend, data is counted in outknt flagprint = 1; %change to 1 for printing and plotting x = x(: ); lx = length(x); outknt = zeros(2,1); xknt = zeros(nbins,1); lindx=0; indx=find(x < = xend(1)); lindx=length(indx); if(lindx ~= 0); outknt(1)=lindx; end x(indx)=[]; lindx=0; indx=find(x > xend(2)); lindx=length(indx); if(lindx ~= 0); outknt(2)=lindx; end x(indx)=[]; xdelta = (xend(2)-xend(1))/nbins; xbin = xend(1) + [0: nbins]*xdelta; xcenter = zeros(nbins,1); % loop over the few bins, not over the many data for ibin=[1: nbins]; % loop over bins, not data lindx=0; indx=find( (xbin(ibin)< x)& ( x < =xbin(ibin+1)) ); lindx=length(indx); xcenter(ibin) = mean([xbin(ibin) xbin(ibin+1)]); if(lindx~=0); xknt(ibin)=lindx; end%%x(indx)=[]; end %disp([ibin, xbin(ibin) xbin(ibin+1) xcenter(ibin) xknt(ibin)]) end if(flagprint==1); format bank disp([' binid lowedge upedge center count']) for ibin=[1: nbins]; % loop over bins, not data disp([ibin, xbin(ibin) xbin(ibin+1) xcenter(ibin) xknt(ibin)]) end end format short e if(flagprint==1); plot( xcenter, xknt,'r*-'); grid end

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