{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Test2-Solutions-S09

# Test2-Solutions-S09 - 1 22 marks In a particular soccer...

This preview shows pages 1–3. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1. ( 22 marks ) In a particular soccer league, a study has shown that 40% of the players are below average (with risk parameter & 1 ) and 60% are above average (with risk parameter & 2 ). Let X j represent the number of goals scored in game j by a chosen soccer player ( j = 1 ; 2 ; ::: ). It is assumed that Pr ( X j = x j j & = & 1 ) = e & 1 x j ! , x j = 0 ; 1 ; ::: and Pr ( X j = x j j & = & 2 ) = 1 4 e & 1 x j ! + 3 4 e & 2 2 x j x j ! , x j = 0 ; 1 ; ::: Conditional on the risk parameter & , the r.v.&s X 1 ; X 2 ; ::: are all independent. A given soccer player have scored 1 goal in game 1 and 2 goals in game 2 . (a) ( 6 marks ) Compute the hypothetical means and process variances for both types of soccer player. Solution: For the hypothetical means, ¡ ( & 1 ) = E [ X j j & = & 1 ] = 1 X x j =0 x j & e & 1 x j ! ¡ = 1 , and ¡ ( & 2 ) = E [ X j j & = & 2 ] = 1 X x j =0 x j & 1 4 e & 1 x j ! + 3 4 e & 2 2 x j x j ! ¡ = 1 4 1 X x j =0 x j e & 1 x j ! + 3 4 1 X x j =0 x j e & 2 2 x j x j ! = 1 4 (1) + 3 4 (2) = 1 : 75 . For the process variances, v ( & 1 ) = V ar ( X j j & = & 1 ) = E ¢ X 2 j j & = & 1 £ & ( ¡ ( & 1 )) 2 = 1 X x j =0 x 2 j e & 1 x j ! & (1) 2 = 2 (1) & (1) 2 = 1 , 1 and v ( & 2 ) = V ar ( X j j & = & 2 ) = E & X 2 j j & = & 2 ¡ & ( ¡ ( & 2 )) 2 = 1 X x j =0 x 2 j ¢ 1 4 e & 1 x j !...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern