MATH 352 Assignment #7 Due: Tuesday December 4, 2007
1. Chapter 7 Problem 24. 2. Chapter 7 Theoretical Exercise 16. 3. Let F be a family of subsets of N = cfw_1, 2, . . . , n that has the property that there are no sets A, B F which satisfy A B . Let = (1
MATH 352 Assignment #6 Due: Friday November 23, 2007
1. Chapter 6 Problem 20. 2. Chapter 6 Theoretical Exercise 9. 3. Chapter 6 Problem 40. 4. Let X U nif (0, 1). Find the pmf of Y if the conditional distribution of Y given X = x 1 is Bin(n, x). Does Y ha
MATH 352 Assignment #4 Due: Tuesday October 30, 2007
1. In class we looked at the following problem: An urn initially contains one red and two green balls. Balls are repeatedly drawn, and each time a ball is drawn, it is replaced into the urn along with a
MATH 352 Assignment #2 Solutions
1. Use the Principle of Inclusion/Exclusion to solve each of the following problems: (a) Find the probability that a permutation of a1 , a1 , a2 , a2 , . . . , an , an will have no identical symbols consecutive. The rst an
MATH 352 Assignment #1 Due: Tuesday September 18, 2007
1. Twenty-two individually carved merry-go-round horses are to be arranged in 2 concentric rings on a merry-go-round. In how many ways can this be done if each ring is to contain 11 horses and each ho
Mathematics 352 Introduction to Probability Fall 2007 Course Outline
Instructor: Office:
Dr. Jill Simmons Clearihue D229 (721-7451, jills at uvic dot ca)
Office Hours: Mondays 1:00-2:00, Tuesdays 2:30-3:30, and Thursdays 11:30-1:00 Web Page: http:/www.mat
MATH 352 Practice Inclusion / Exclusion Problem
If 11 identical items are randomly distributed amongst 3 labelled boxes, what is the probability that box 1 gets no more than 3, box 2 gets no more than 4, and box 3 gets no more than 6 items?
Hint 1: Let A1
Inclusion - Exclusion
Theorem: For occur simultaneously. Then let denote the event that exactly m among the events , where .
(Note that the formula for Proof: Let events of the form
contains
summands.) possible let
be the partition of the sample space det
MATH 352 Solution to Practice Inclusion / Exclusion Problem
If 11 identical items are randomly distributed amongst 3 labelled boxes, what is the probability that box 1 gets no more than 3, box 2 gets no more than 4, and box 3 gets no more than 6 items? So
MATH 352 - FORMULA SHEET
N
P (exactly m of N Ai events occur) = P (at least m of N Ai events occur) = where Sk =
1j1 <jk N
k =m N
(1)km (1)km
k m
Sk , Sk ,
k =m
k 1 m 1
P (Aj1 Aj2 Ajk )
DISCRETE DISTRIBUTIONS
Name Bernoulli(p) Binomial(n, p) Geometric(p)