Covariance and Correlation for Regression Model

[Rupert]

I've been looking over some regression models lately and I came across one which, although similar, differs from the "standard" simple linear model. I was hoping somebody could provide some assistance with some properties that I'm confused with.

Assuming the regression form:



with expected value:



where and

and, from what I've worked out:

,

and:
, **, **

**These could be wrong.

How can it be shown that:

(a)



I know that the covariance formula is given by:



However, I'm confused about how to manipulate this formula to yield the desired result.

(b)



Here, I know that if it can be shown that:



it follows that:



However, as in part (a), I'm confused about how to develop the covariance formula accordingly.

Thanks!