Suppose and are two random variables with E( ) = E( ) = 0. Show that var( ) = E( 2) and cov(

Suppose ξ and ζ are two random variables with E(ξ ) = E(ζ ) = 0.

Show that var(ξ ) = E(ξ 2) and cov(ξ , ζ ) = E(ξ ζ ).

Notes. More generally, var(ξ ) = E(ξ 2) − [E(ξ )]

2 and cov(ξ , ζ ) =

E(ξ ζ ) − E(ξ )E(ζ ).