{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Ass4sol - STAT 330 Assignment 4 Solutions 1 a By...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT 330 Assignment 4 Solutions 1. a. By independence, the joint distribution of Y 1 and Y 2 is the product of the two marginal densities: β α α β α α α α / ) ( 1 2 1 1 ) ( ) ( 1 2 1 2 1 2 1 2 1 1 ) , ( x x e x x x x f a + Γ Γ + = , x 1 0, x 2 0. With U and V as defined, we have that x 1 = u 1 u 2 and x 2 = u 2 (1– u 1 ). Thus, the Jacobian of transformation J = u 2. Thus, the joint density of U 1 and U 2 is 2 / 1 1 2 1 2 1 ) ( ) ( 1 2 1 2 2 1 2 1 1 )] 1 ( [ ) ( ) , ( u e u u u u u u f u a β α α β α Γ α Γ = α + α β α + α α α β α Γ α Γ = α + α / 1 2 1 1 1 1 ) ( ) ( 1 2 2 1 2 1 2 1 1 ) 1 ( u e u u u a , with 0 < u 1 < 1, and u 2 > 0. b. 1 1 1 1 ) ( ) ( ) ( / 1 0 1 1 1 1 1 ) ( ) ( 1 1 2 1 1 1 2 1 2 1 2 1 1 1 ) 1 ( ) 1 ( ) ( α α α Γ α Γ α + α Γ β α + α β α α α Γ α Γ = = α + α u u dv e v u u u f a a a v U , with 0 < u 1 < 1. This is the beta density as defined. c. β α + α α + α Γ β α α α Γ α Γ β α + α β α + α α + α = = / 1 2 ) ( 1 1 1 0 1 1 1 1 ) ( ) ( 1 / 1 2 1 2 2 2 1 2 1 2 1 2 1 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern