The Mystery of the ARROW: Can Someone Explain?

In summary, the conversation discussed the derivation of the ARROW formula and how it involves completing the square and separating the exponentials. The final result involves factoring out y^2 in the last exponential term. The individual involved in the conversation expressed their gratitude for the explanation."
  • #1
tuanle007
36
0
can someone explain to me how did it derived to the ARROW...
I am not quite sure how that happened.thanks
 

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  • #2
You have
[tex]e^{-\frac{x^2+ y^2- 2\rho xy}{2\sigma(1-\rho)^2}}[/itex]
They complete the square:
[tex]x^2- 2\rho xy+ \rho^2y^2- \rho^2y^2+ y^2= (x- \rho y)^2+ (y^2- \rho^2 y^2)[/tex]
so the exponential becomes
[tex]e^{-\frac{(x-\rho y)^2- (y^2- \rho^2 y^2)}{2\sigma(1-\rho)^2}}[/itex]
Then separate the exponentials:
[tex]e^{-\frac{(x- \rho y)^2}{2\sigma(1-\rho)^2}}e^{-\frac{(y^2- \rho^2 y^2}{2\sigma(1-\rho)^2}}[/tex]
and finally factor out y2 in the last exponential
[tex]e^{-\frac{(x- \rho y)^2}{2\sigma(1-\rho)^2}}e^{-\frac{y^2(1- \rho^2}{2\sigma(1-\rho)^2}}[/tex]
 
  • #3
Thank You So Much!
 

1. What is the mystery of the ARROW?

The mystery of the ARROW refers to the unexplained phenomenon of an arrow seemingly moving in a circular motion on its own without any external force. This has puzzled scientists and researchers for many years.

2. How does the ARROW move without any external force?

There are several theories that attempt to explain the movement of the ARROW. Some suggest it could be due to magnetic fields or air currents, while others propose that it could be a result of static electricity or even quantum effects.

3. Is there any scientific evidence to support these theories?

While there have been many experiments and studies conducted on the ARROW, there is still no conclusive evidence to support any one theory. Scientists continue to research and investigate this mystery in hopes of finding a definitive answer.

4. Can the ARROW phenomenon be replicated in a controlled environment?

Yes, there have been experiments where scientists have successfully replicated the ARROW phenomenon using various materials and techniques. However, these experiments have not been able to provide a clear explanation for the mystery.

5. What are the potential applications of understanding the mystery of the ARROW?

If we are able to understand the underlying cause of the ARROW phenomenon, it could have significant implications in fields such as engineering, physics, and even technology. It could also help us better understand the laws of nature and the mysteries of the universe.

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