N
nicolathompson
Member
Hi,
I'm confused about the equations for variance.
We have:
var(X+Y) = var(X) + var(Y) if X and Y independent
var(nX) = (n^2)var(X)
But in chapter 7 compound distributions:
S= X1 + X2 + ... + XN
var(S given N=n) = nvar(X) WHY NOT (n^2)var(X)?
For example, say n=3. Then since all Xs are iid rvs, isn't var(S given N=3) just
var(X+X+X) = var(3X) = 9var(X)?
I'm confused about the equations for variance.
We have:
var(X+Y) = var(X) + var(Y) if X and Y independent
var(nX) = (n^2)var(X)
But in chapter 7 compound distributions:
S= X1 + X2 + ... + XN
var(S given N=n) = nvar(X) WHY NOT (n^2)var(X)?
For example, say n=3. Then since all Xs are iid rvs, isn't var(S given N=3) just
var(X+X+X) = var(3X) = 9var(X)?