## Systematic component variation

The appendix of the paper of [McPherson et al (1982) contains a derivation of the systematic component variation SCV. I understand the derivation with exception of the first step. Here are the premisses:

: observed cases in region i
: expected cases in region i
: multiplicative factor associated with region i (I suppose it means )

Now the following assumptions have been done:

is approximately Poisson distributed with mean
is considered as a random variable with expected value and variance .

From these the following formula is concluded:

var() = +

It tried to find out how to get the formula by the given premisses and assumptions and didn't succeed. Any idea? Thanks for help.