Proof help plz

[nervedbaby]

I took the introduction of probability four years ago and I really can't remember how to solve this.
Is there any hint on how should I start?
Thanks

 

[BGM]

The very first step could be expanding the square, then solve for the moments. In the latter parts of the question you will need more knowledge about the definitions and properties of mean, variance, covariance etc. Lets try first.