# Systematic component variation

#### giordano

##### New Member
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:

$$O_i$$: observed cases in region i
$$E_i$$: expected cases in region i
$$\lambda_i$$: multiplicative factor associated with region i (I suppose it means $$O_i=\lambda_i*E_i$$)

Now the following assumptions have been done:

$$O_i$$ is approximately Poisson distributed with mean $$\lambda_iE_i$$
$$\lambda_i$$ is considered as a random variable with expected value $$1$$ and variance $$\sigma^2$$.

From these the following formula is concluded:

var($$O_i$$) = $$E_i^2\sigma^2$$ + $$E_i$$

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.