This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Probability for Engineering Applications Assignment #3, due at the beginning of class on Thursday, February 9 th , 2006 1. (2 pts) (Textbook exercise 2.47) In this problem we derive the multinomial coeffi cient. Suppose we partition a set of n distinct objects into m subsets B 1 , B 2 , , B m of size k 1 , k 2 , , k m , respectively, where k i i and k 1 + k 2 + + k m = n . a. Let N i denote the number of possible outcomes when the i th subset is selected. Show that N 1 = n k 1 ! , N 2 = n k 1 k 2 ! , , N m 1 = n k 1  k m 2 k m 1 ! , N m = 1 Basically we are interested in the following: We have a total on n objects. From these, we first pick k 1 objects. How many ways of doing this (denote this by N 1 )? From the remaining objects, we now pick k 2 objects. How many ways of doing this (denote this by N 2 )? And so on. b. Show that the total number of partitions is then N 1 N 2 N m = n !...
View
Full
Document
This note was uploaded on 09/07/2009 for the course ECE 302 taught by Professor Gelfand during the Fall '08 term at Purdue UniversityWest Lafayette.
 Fall '08
 GELFAND

Click to edit the document details