"Linearity of variance" holds only if Yi is assumed to be independent.
hershg
We can simplify our variance expression by the assumption that each Yi sample is i.i.d. (independent and identically distributed) which is a fair assumption in our case.
moridin22
In particular it's not even an assumption, we are actually drawing independent samples from the same distribution, so the Yi really are i.i.d.
keirp
Is there a situation in which we might want dependent samples? For instance, to ensure ample coverage of the light sources?
killawhale2
Well, in any case, this slide is talking about properties for general RVs, which means that the linearity of variance is not guaranteed.
"Linearity of variance" holds only if Yi is assumed to be independent.
We can simplify our variance expression by the assumption that each Yi sample is i.i.d. (independent and identically distributed) which is a fair assumption in our case.
In particular it's not even an assumption, we are actually drawing independent samples from the same distribution, so the Yi really are i.i.d.
Is there a situation in which we might want dependent samples? For instance, to ensure ample coverage of the light sources?
Well, in any case, this slide is talking about properties for general RVs, which means that the linearity of variance is not guaranteed.