1.3 lecture03

1.3 lecture03 - STAT 1301 Probability & Statistics...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 STAT 1301 Lecture 3 Unordered selection with replacement: Three Dice The casino game big-small is a casino game played with three dice. How many unordered outcomes are there? It is a typical example of counting the number of unordered subsets (3 numbers) from a set of distinguishable objects (faces 1 – 6) with replacement as there can be more than one die landing on the same number (e.g. {1, 1, 3}, {6, 6, 6}, etc). Different orderings of the numbers are treated as the same outcome (e.g. {1, 2, 3} is the same as {2, 1, 3}, {4, 5, 5} is the same as {5, 4, 5}, etc). If a set of n indistinguishable objects is to be partitioned into r distinguishable groups groups.
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Example 20 red balls are distributed into 4 urns. How many different partitions are possible? Review Sample spaces with equally likely outcomes. Counting techniques Product rule Permutation Combination Properties A combinatorial Identity: . 1 , 1 1 1 n k k n k n k n The Binomial Theorem: An Identity: . ) ( 0 k n k n k n y x k n y x . 2 0 n n k k n Multinomial A set of n distinct items is to be divided into r distinct groups of respective size n 1 , n 2 , …, n r , where n i = n. How many different divisions are possible? r
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the 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 / 6

1.3 lecture03 - STAT 1301 Probability & Statistics...

This preview shows document pages 1 - 3. Sign up to view the full document.

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