how to create two bell shape curves

with the areas under these curves equal to 1, the same mean but different standard deviations. Thanks!

Answer 1

[Wayne King]

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')

Answer 2

[jenka]

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

Answer 3

[Wayne King]

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)

[jenka]

But of course:) He-he....