MATLAB: How to create two bell shape curves

gaussian

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

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')

If you have the Statistics Toolbox, then this is extremely easy, just using the normpdf function which encodes the formula for you.

MU    = 10;
SIGMA = 1;
x = 5 : 0.01 : 15;
y = normpdf(x,MU,SIGMA)
figure
plot(x,y)

If you don't have the toolbox, then just use

y =1./sqrt(2*pi*SIGMA) * exp(-(x-MU).^2 /(2 * SIGMA));

instead.

x = [-3:.1:3];
y = normpdf(x,0,1);
y2 = normpdf(x,0,0.5);
plot(x,y,x,y2)

More info:https://es.mathworks.com/help/stats/normal-distribution.html