Suppose i, i are random variables for i = 1,...,n. As pairs, they are independent and identically

Suppose ξi, ζi are random variables for i = 1,...,n. As pairs, they are independent and identically distributed in i. Let ξ = 1 n

n i=1 ξi, and likewise for ζ . True or false, and explain:

(a) cov(ξi, ζi) is the same for every i.

(b) cov(ξi, ζi) = 1 n

n i=1(ξi − ξ )(ζi − ζ ).