HW4-sol (Math 425) - = 2 } = 5 10 5 9 P { X = 3 } = 5 10 4...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 425 – Section 008 Homework 4 – Chapter 4, problems 1, 4, 18 Problem 4. Five men and 5 women are ranked according to their scores on an examination. Assume that no two scores are alike and all 10! possible rankings are equally likely. Let X denote the highest ranking achieved by a woman. Find P { X = i } , i = 1 ,..., 10. Solution. Clearly, P { X > 6 } = 0. Now, suppose that X = i . This means that the first i - 1 ranked individuals are men, and the i th ranked is a woman. By using the multiplication rule, we get: P { X = 1 } = 5 10 P { X
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = 2 } = 5 10 5 9 P { X = 3 } = 5 10 4 9 5 8 P { X = 4 } = 5 10 4 9 3 8 5 7 P { X = 5 } = 5 10 4 9 3 8 2 7 5 6 P { X = 6 } = 5 10 4 9 3 8 2 7 1 6 5 5 Alternative solution. Consider the event X i . It is equivalent to saying that the top i-1 individuals are men. Hence, P { X i } = ( 5 i-1 ) ( 10 i-1 ) Now, P { X = i } = P { X i } -P { X i + 1 } = ( 5 i-1 ) ( 10 i-1 )-( 5 i ) ( 10 i ) 1...
View Full Document

Ask a homework question - tutors are online