2 Example Class 1

2 Example Class 1 - THE UNIVERSITY OF HONG KONG DEPARTMENT...

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: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 PROBABILITY AND STATISTICS I EXAMPLE CLASS 1 Review Combinatorial Analysis (a) Multiplication Principle (b) Selection of r from n distinct objects: With replacement Without replacement Ordered n r n P r = n ! ( n- r )! Unordered ( n + r- 1 r ) = ( n + r- 1)! r ! × ( n- 1)! ( n r ) = n ! r ! × ( n- r )! (c) Arrangement of n objects, with r distinct types. In other words, there are n 1 objects of type 1, n 2 objects of type 2, ..., n r objects of type r . (e.g. number of different letter arrangements can be formed using the letters STATISTICS.) n ! n 1 ! × n 2 ! × ··· × n r ! (d) Partition of n distinct objects into r distinct groups with specified size n 1 ,n 2 , ··· ,n r . (e.g. number of ways in dividing a class of 40 into groups of 10, 10 and 20.) n n 1 ,n 2 , ··· ,n r = n ! n 1 ! × n 2 ! × ··· × n r ! (e) Partition of n indistinguishable objects into r distinct groups (i.e. we only concern the number of objects in each group)....
View Full Document

This note was uploaded on 05/04/2011 for the course STAT 1301 taught by Professor Smslee during the Spring '08 term at HKU.

Page1 / 3

2 Example Class 1 - THE UNIVERSITY OF HONG KONG DEPARTMENT...

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