hw8sol_fall03

# hw8sol_fall03 - AMS 310.01 FALL 2003 Homework#8 Solutions...

• Homework Help
• PresidentHackerCaribou10582
• 3

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

AMS 310.01  FALL 2003   Homework #8  Solutions  2.48 Let  i i x cu a = + . Then 1 1 1 1 ( ) n n n i i i i i i x u na x cu a c cu a n n n n = = = = = + = + = + Now, 2 2 2 2 2 2 2 2 1 1 1 1 ( ) ( ) ( ) ( ) ( 1) ( 1) ( 1) ( 1) n n n n i i i i x u i i i i x x cu a cu a cu cu u u s c c s n n n n = = = = - + - - - - = = = = = - - - - Thus,  x u s c s = 5.72 (a) The independent random variables  1 2 and X X have the same probability distribution  ( ;2,0.3) b x Hence the joint probability distribution of  1 2 and X X  is 1 2 1 2 ( , ) ( ;2,0.3) ( ;2,0.3) f x x b x b x =                 1 1 2 2 1 2 1 2 2 2 4 1 2 1 2 2 2 2 2 (0.3) (0.7) (0.3) (0.7) (0.3) (0.7) x x x x x x x x x x x x - - + - - � � � � � �� � = = � � � � � �� � � � � � � �� � where  1 2 0,1,2, and 0,1,2. x x = = (b)  1 2 ( ) (0,1) (0,2) (1,2) P X X f f f < = + +                           1 3 2 2 3 1 2 2 2 2 2 2 (0.3) (0.7) (0.3) (0.7) (0.3) (0.7) 0 1 0 2 1 2 ���� ���� ���� = + + ���� ���� ���� ���� ���� ����                          = 0.2058 + 0.0441 + 0.0378  =  0.2877

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

This is the end of the preview. Sign up to access the rest of the document.
• Fall '03
• Mendell

{[ 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