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

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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...
View Full Document

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online