Easy problem

  • Thread starter tuanle007
  • Start date
36
0

Main Question or Discussion Point

can someone explain to me how did it derived to the ARROW...
I am not quite sure how that happened.thanks
 

Attachments

Answers and Replies

HallsofIvy
Science Advisor
Homework Helper
41,738
897
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]
 
36
0
Thank You So Much!!!
 

Related Threads for: Easy problem

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
2K
Replies
0
Views
2K
Replies
1
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
5K
  • Last Post
Replies
1
Views
2K
Top