Solution Found!
How big or small can Cov(Y1, Y2) be? Use the fact that ?2
Chapter 5, Problem 98E(choose chapter or problem)
How big or small can \({Cov}\left(Y_{1}, Y_{2}\right)\) be? Use the fact that \(\rho^{2} \leq 1\) to show that
\(-\sqrt{V\left(Y_{1}\right) \times V\left(Y_{2}\right)} \leq \operatorname{Cov}\left(Y_{1}, Y_{2}\right) \leq \sqrt{V\left(Y_{1}\right) \times V\left(Y_{2}\right)}\)
Equation Transcription:
Text Transcription:
Cov(Y_1,Y_2)
rho^2 leq 1
-sqrt V(Y_1)xV(Y_2)Cov(Y_1,Y_2)Vx(Y_1)V(Y_2)
Questions & Answers
QUESTION:
How big or small can \({Cov}\left(Y_{1}, Y_{2}\right)\) be? Use the fact that \(\rho^{2} \leq 1\) to show that
\(-\sqrt{V\left(Y_{1}\right) \times V\left(Y_{2}\right)} \leq \operatorname{Cov}\left(Y_{1}, Y_{2}\right) \leq \sqrt{V\left(Y_{1}\right) \times V\left(Y_{2}\right)}\)
Equation Transcription:
Text Transcription:
Cov(Y_1,Y_2)
rho^2 leq 1
-sqrt V(Y_1)xV(Y_2)Cov(Y_1,Y_2)Vx(Y_1)V(Y_2)
ANSWER:
Solution 98E
Step1 of 2:
We have Let us consider a random variables ().
We need to show that,
Step2 of 2:
The coefficient of correlation is defined as: