Solution Found!
Let Y1, Y2, . . . be a sequence of random variables with
Chapter 9, Problem 35E(choose chapter or problem)
Let \(Y_{1}, Y_{2}, \ldots\) be a sequence of random variables with \(E\left(Y_{i}\right)=\mu\) and \(V\left(Y_{i}\right)=\sigma_{i}^{2}\). Notice that the \(\sigma_{i}^{2,}\)s are not all equal.
a. What is \(E\left(\bar{Y}_{n}\right)\)?
b. What is \(V\left(\bar{Y}_{n}\right)\)?
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 \(\mu\)?
Equation Transcription:
Text Transcription:
Y_1, Y_2, ….
E(Y_i) = mu
V(Y_i) = sigma_{i}^{2}
sigma_{i}^{2,}
E(bar{Y}_{n})
V(bar{Y}_{n})
sigma_{i}^{2,}
bar{Y}_{n}
mu
Questions & Answers
QUESTION:
Let \(Y_{1}, Y_{2}, \ldots\) be a sequence of random variables with \(E\left(Y_{i}\right)=\mu\) and \(V\left(Y_{i}\right)=\sigma_{i}^{2}\). Notice that the \(\sigma_{i}^{2,}\)s are not all equal.
a. What is \(E\left(\bar{Y}_{n}\right)\)?
b. What is \(V\left(\bar{Y}_{n}\right)\)?
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 \(\mu\)?
Equation Transcription:
Text Transcription:
Y_1, Y_2, ….
E(Y_i) = mu
V(Y_i) = sigma_{i}^{2}
sigma_{i}^{2,}
E(bar{Y}_{n})
V(bar{Y}_{n})
sigma_{i}^{2,}
bar{Y}_{n}
mu
ANSWER:Step 1 of 3
(a)
Using 
