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how to create two bell shape curves

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jenka
jenka 2013-4-24
with the areas under these curves equal to 1, the same mean but different standard deviations. Thanks!

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Wayne King
Wayne King 2013-4-24
编辑：Wayne King 2013-4-24
Do you have the Statistics Toolbox?
x = -10:0.01:10;
y = normpdf(x,0,1);
y1 = normpdf(x,0,sqrt(2));
If you do not have the Statistics Toolbox, you can just use the definition of the Gaussian
f = @(x) 1/sqrt(2*pi)*exp(-x.^2/2);
integral(f,-10,10)
g = @(x) 1/sqrt(2*pi*2)*exp(-x.^2/4);
integral(g,-10,10)
To see the curves for above:
fcurv = 1/sqrt(2*pi)*exp(-x.^2/2);
gcurv = 1/sqrt(2*pi*2)*exp(-x.^2/4);
plot(x,fcurv); hold on;
plot(x,gcurv,'r')

更多回答（2 个）

jenka
jenka 2013-4-24
Hi Wayne, yes, I tried both ways already. However, if you do sum(y) or sum(y1) to give you the are under the curve (or trapz(y)), it does not give you 1. That is why I posted here. I need the area under the curves to be equal to one. Any suggestions? Thanks
Wayne King
Wayne King 2013-4-24
Hi Jenka, you cannot just do sum(y), you are forgetting about the very important dx in the integral
x = -10:0.01:10;
y = normpdf(x,0,1);
y1 = normpdf(x,0,sqrt(2));
dx = mean(diff(x));
sum(y*dx)
sum(y1*dx)

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