Covariance of the population SxyU


New Member
Hey, I need some help to figure out this problem!

I'm asked to express SxyU, the covariance of the population, as a function of four totals and propose an estimator based on this result.

I started something, but as you will see, I only have 3 totals and I'm not even sure of what I did. Should I express N as a total too? Then, I have no idea what to propose as estimator for SxyU.
Screen Shot 2020-12-17 at 5.20.04 PM.png

Then, how would you prove this relation with Taylor linearization?

Screen Shot 2020-12-17 at 5.27.35 PM.png

Thank you for your help!