Chapter 9.3, Problem 35E

Let Y₁, Y₂,… be a sequence of random variables with E(Y_i) = μ and $V(Y_i)={\sigma }_i^2$. Notice that the ${\sigma }_i^2$’s are not all equal.

a What is $E({\bar{Y}}_n)$?

b What is $V({\bar{Y}}_n)$?

c Under what condition (on the ${\sigma }_i^2$’s) can Theorem 9.1 be applied to show that ${\bar{Y}}_n$ is a consistent estimator for μ?