Numerically approximate the MLE by evaluating function

Hi!

I have a problem with the following exercice:

I wrote this command but I'm not sure if it's correct, for example the interval is different because -10 belongs to the interval...Someone could help me please?

Thank you!

x=[-10:0.02:10]
y=exp(-(x-1).^2./2)+3.*exp(-(x-2).^2./2)
plot(x,y)

Answer 1

[Thiago Henrique Gomes Lobato]

If you want to make sure -10 is not in the interval and still get equidistant points you could do something like this (it actually doesn't matter in this example since there's no discontinuity):

x=linspace(-9.9999,10,1000);
y=exp(-(x-1).^2./2)+3.*exp(-(x-5).^2./2);
plot(x,y)

Otherwise everything seems fine with except of the mean in the second equation that you wrote -2 and not -5 as in the command. This is basically the sum of two gaussians with same variance and mean 1 and 5 where the second one has a bigger weighting.