statistics and probability problem by Matlab

Number machine

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press the button, get a number

Number machine output

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button push

Is there a pattern?

Number machine output

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button push

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Is there a pattern?

The idea of a histogram

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v(t)

The idea of a histogram

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The idea of a histogram

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quantization

The idea of a histogram

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The idea of a histogram

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Number machine output

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button push

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Histogram

Number machine output

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Histogram

normalize to the total number of button presses

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Histogram

use more button pushes and more bins

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Histogram

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Histogram

Matlab script % ECE399 example_001 % generate and plot some random samples; create histograms % 03/19/13 D D Duncan % N = 1000; x = rand(1,N); figure(1);plot(x(1:100),'r.') ylabel('number value');xlabel('button push') numbins = 10; [num,bincen] = hist(x,numbins); figure(2);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') x = 0.5+0.1*randn(1,N); figure(3);plot(x(1:100),'r.');ylim([0 1]); xlabel('button push');ylabel('number value') [num,bincen] = hist(x,numbins); figure(4);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') % variations figure(5);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') N = 100000; x = 0.5+0.1*randn(1,N); numbins = 100; [num,bincen] = hist(x,numbins); figure(6);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') figure(7);plot(bincen,num/N,'r-');xlim([0 1]) xlabel('x value');ylabel('fraction of values')

% ECE399 example_001 % generate and plot some random samples; create histograms % 03/19/13 D D Duncan % N = 1000; x = rand(1,N); figure(1);plot(x(1:100),'r.') ylabel('number value');xlabel('button push') numbins = 10; [num,bincen] = hist(x,numbins); figure(2);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') x = 0.5+0.1*randn(1,N); figure(3);plot(x(1:100),'r.');ylim([0 1]); xlabel('button push');ylabel('number value') [num,bincen] = hist(x,numbins); figure(4);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') % variations figure(5);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') N = 100000; x = 0.5+0.1*randn(1,N); numbins = 100; [num,bincen] = hist(x,numbins); figure(6);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') figure(7);plot(bincen,num/N,'r-');xlim([0 1]) xlabel('x value');ylabel('fraction of values')

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% ECE399 example_001 % generate and plot some random samples; create histograms % 03/19/13 D D Duncan % N = 1000; x = rand(1,N); figure(1);plot(x(1:100),'r.') ylabel('number value');xlabel('button push') numbins = 10; [num,bincen] = hist(x,numbins); figure(2);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') x = 0.5+0.1*randn(1,N); figure(3);plot(x(1:100),'r.');ylim([0 1]); xlabel('button push');ylabel('number value') [num,bincen] = hist(x,numbins); figure(4);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') % variations figure(5);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') N = 100000; x = 0.5+0.1*randn(1,N); numbins = 100; [num,bincen] = hist(x,numbins); figure(6);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') figure(7);plot(bincen,num/N,'r-');xlim([0 1]) xlabel('x value');ylabel('fraction of values')

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% ECE399 example_001 % generate and plot some random samples; create histograms % 03/19/13 D D Duncan % N = 1000; x = rand(1,N); figure(1);plot(x(1:100),'r.') ylabel('number value');xlabel('button push') numbins = 10; [num,bincen] = hist(x,numbins); figure(2);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') x = 0.5+0.1*randn(1,N); figure(3);plot(x(1:100),'r.');ylim([0 1]); xlabel('button push');ylabel('number value') [num,bincen] = hist(x,numbins); figure(4);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') % variations figure(5);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') N = 100000; x = 0.5+0.1*randn(1,N); numbins = 100; [num,bincen] = hist(x,numbins); figure(6);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') figure(7);plot(bincen,num/N,'r-');xlim([0 1]) xlabel('x value');ylabel('fraction of values')

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% ECE399 example_001 % generate and plot some random samples; create histograms % 03/19/13 D D Duncan % N = 1000; x = rand(1,N); figure(1);plot(x(1:100),'r.') ylabel('number value');xlabel('button push') numbins = 10; [num,bincen] = hist(x,numbins); figure(2);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') x = 0.5+0.1*randn(1,N); figure(3);plot(x(1:100),'r.');ylim([0 1]); xlabel('button push');ylabel('number value') [num,bincen] = hist(x,numbins); figure(4);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') % variations figure(5);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') N = 100000; x = 0.5+0.1*randn(1,N); numbins = 100; [num,bincen] = hist(x,numbins); figure(6);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') figure(7);plot(bincen,num/N,'r-');xlim([0 1]) xlabel('x value');ylabel('fraction of values')

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% ECE399 example_001 % generate and plot some random samples; create histograms % 03/19/13 D D Duncan % N = 1000; x = rand(1,N); figure(1);plot(x(1:100),'r.') ylabel('number value');xlabel('button push') numbins = 10; [num,bincen] = hist(x,numbins); figure(2);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') x = 0.5+0.1*randn(1,N); figure(3);plot(x(1:100),'r.');ylim([0 1]); xlabel('button push');ylabel('number value') [num,bincen] = hist(x,numbins); figure(4);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') % variations figure(5);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') N = 100000; x = 0.5+0.1*randn(1,N); numbins = 100; [num,bincen] = hist(x,numbins); figure(6);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') figure(7);plot(bincen,num/N,'r-');xlim([0 1]) xlabel('x value');ylabel('fraction of values')

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% ECE399 example_001 % generate and plot some random samples; create histograms % 03/19/13 D D Duncan % N = 1000; x = rand(1,N); figure(1);plot(x(1:100),'r.') ylabel('number value');xlabel('button push') numbins = 10; [num,bincen] = hist(x,numbins); figure(2);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') x = 0.5+0.1*randn(1,N); figure(3);plot(x(1:100),'r.');ylim([0 1]); xlabel('button push');ylabel('number value') [num,bincen] = hist(x,numbins); figure(4);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') % variations figure(5);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') N = 100000; x = 0.5+0.1*randn(1,N); numbins = 100; [num,bincen] = hist(x,numbins); figure(6);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') figure(7);plot(bincen,num/N,'r-');xlim([0 1]) xlabel('x value');ylabel('fraction of values')

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% ECE399 example_001 % generate and plot some random samples; create histograms % 03/19/13 D D Duncan % N = 1000; x = rand(1,N); figure(1);plot(x(1:100),'r.') ylabel('number value');xlabel('button push') numbins = 10; [num,bincen] = hist(x,numbins); figure(2);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') x = 0.5+0.1*randn(1,N); figure(3);plot(x(1:100),'r.');ylim([0 1]); xlabel('button push');ylabel('number value') [num,bincen] = hist(x,numbins); figure(4);bar(bincen,num);xlim([0 1]) xlabel('x value');ylabel('number of values') % variations figure(5);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') N = 100000; x = 0.5+0.1*randn(1,N); numbins = 100; [num,bincen] = hist(x,numbins); figure(6);bar(bincen,num/N);xlim([0 1]) xlabel('x value');ylabel('fraction of values') figure(7);plot(bincen,num/N,'r-');xlim([0 1]) xlabel('x value');ylabel('fraction of values')

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