Scaling of Normal distribution - area under 'nompdf'

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Arwel
Arwel 2024-9-24
评论： Star Strider 2024-9-24
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?

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Star Strider
Star Strider 2024-9-24
Ran in:
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
.

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