Solution Found!
Let Xi be as in but with E(Xi ) = i and n1n i=1 i . Show
Chapter , Problem 2(choose chapter or problem)
QUESTION:
Let \(X_i\) be as in Problem 1 but with \(E\left(X_{i}\right)=\mu_{i}\) and \(n^{-1} \sum_{i=1}^{n} \mu_{i} \rightarrow \mu\). Show that \(\bar{X} \rightarrow \mu\) in probability.
Questions & Answers
QUESTION:
Let \(X_i\) be as in Problem 1 but with \(E\left(X_{i}\right)=\mu_{i}\) and \(n^{-1} \sum_{i=1}^{n} \mu_{i} \rightarrow \mu\). Show that \(\bar{X} \rightarrow \mu\) in probability.
ANSWER:Step 1 of 4
We are given that are independent random variables such that
and . Also, we are given that
We need to prove that
(this means that converges to in probability).