Scaling of Normal distribution - area under 'nompdf'

Hi,

I have a simple question which I can't quite see how to figure out and it's bugging me....

As I understand it, the area under 'normpdf' should be unity (as it's a probability). So, if I do the following, it seems to check out...

z = -10:10;
a = 3;
g = normpdf(z,0,a);
trapz(g)

..gives 0.999, which is fine.

However if I simply make a finer 'mesh' on my z array, so....

z = -10:0.5:10;
a = 3;
g = normpdf(z,0,a);
trapz(g)

..this time I get 1.9982.

Clearly, there's some scaling going on.

I though the whole point of 'normpdf' was that it was always normalised. What am I missing here? What is the area under the second curve not = 1?

Answer 1

[Star Strider]

The trapz function can take the independent variable value as the fiirst argument (it otherwise assumes a step size of unity).

Doing that produces something similar to the correct value —

z = -10:0.5:10;
a = 3;
g = normpdf(z,0,a);
trapz(z,g)

ans = 0.9991

.

[Arwel]

A thanks - that makes sense!

[Star Strider]

As always, my pleasure!