{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW5-sol (Math 425)

# HW5-sol (Math 425) - Math 425 Section 008 Homework 5...

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

Math 425 – Section 008 Homework 5 – Chapter 4, problems 14, 22(a), 30, 35, 36, 38, 41, 43, 48 Problem 14. Five distinct numbers are randomly distributed to players num- bered 1 to 5. Whenever two players compare their numbers, the one with the higher one is declared the winner. Initially, player 1 and 2 compare their num- bers; the winner then compares with player 3, and so on. Let X denote the number of times player 1 is a winner. Find P { X = i } , i = 0 , 1 , . . . , 4 . Solution. Notice that X i if and only if player 1 has the card of highest rank among players 1 , 2 , . . . i + 1. The probability of such an event is 1 i +1 . So P { X i } = 1 i + 1 , i = 0 , 1 , . . . , 4 Now, p ( i ) = P { X = i } = P { X i } - P { X i + 1 } Hence, p (0) = 1 - 1 2 ; p (1) = 1 2 - 1 3 ; p (2) = 1 3 - 1 4 ; p (3) = 1 4 - 1 5 ; p (4) = 1 5 . Problem. 22(a) Suppose that two teams play a series of games that end when one of them has won i games. Suppose that each game played, is, indepedently, won by team A with probability p . Find the expected number of games that are played when i = 2. Show that the number is maximized when p = 1 2 .

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.

{[ 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