This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: N (0 ; 2 ) random variables. (1) Find the joint distribution of Y 1 and Y 2 , where Y 1 = X 2 1 + X 2 2 and Y 2 = X 1 = p Y 1 : (2) Show that Y 1 and Y 2 are independent. 6. [#4.23, p.195] For X Beta ( &; ) ; and Y Beta ( & + ; ) be independent random variables, &nd the distribution of XY by making the transformation given in (1) and (2) and integrating out V (1) U = XY;V = Y (2) U = XY;V = X=Y 1 7. [#4.27, p.195] Let X & N ( &; 2 ) , and let Y & N ( ; 2 ) : Suppose X and Y are independent. De&ne U = X + Y and V = X Y . Show that U and V are independent normal random variables. Find the distribution of each of them. 8. Suppose X 1 & N (0 ; 1) ;X 2 & N (0 ; 1) and X 1 and X 2 are independent. Find the distribution of X 1 =X 2 . 2...
View Full
Document
 Fall '07
 HONG
 Economics, Econometrics

Click to edit the document details