homework03 - Probability for Engineering Applications...

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: 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 University-West Lafayette.

Page1 / 2

homework03 - Probability for Engineering Applications...

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