Probability and Statistics Math319, Spring 2010 Worksheet 4 February 18, 2010 The Matching Problem At the end of their graduation ceremony, N students throw up their hats in the air to celebrate. When the hats land on the ground, they are completely mixed
Probability and Statistics Math319, Spring 2010 Consequences of the Axioms Jan 28, 2010 (C1) P() = 0. Proof.
(C2) For any nite sequence of mutually exclusive events E1 , E2 , . . . , En ,
n n
P
i=1
Ei
=
i=1
P(Ei ).
Proof.
1
(C3) For every event E , P(E c
Probability and Statistics Math319, Spring 2010 Worksheet 6 April 1, 2010 Gamblers Ruin We consider now a more general version of the Gamblers Ruin problem where each coin ip results in heads with probability p.
1. Then Pi = and, as before, Pi+1 = So, in
Probability and Statistics Math319, Spring 2010 Worksheet 5 March 4, 2010 The Matching Problem (continued) What is the probability that exactly k graduates each pick their own hat (and each of the remaining do not pick their own hat)?
Recall: from before,
Probability and Statistics Math319, Spring 2010 Worksheet 3 February 9, 2010 The Generalized Basic Principle of Counting If r experiments that are to be performed are such that the rst one may result in any of n1 possible outcomes; and if, for any of thes
Math 319, Spring 2010
Quiz 3
Thursday, April 15, 2010 9.05-9.40 am
Name :
No use of notes or textbook - For full credit, show your work - Work alone
1. State the most general version of Bayes Formula, carefully introducing any terms you use.
1
2. (a) Comp
Math 319, Spring 2010
Quiz 2
Thursday, March 4, 2010 9.05-9.40 am
Name :
No use of notes or textbook - For full credit, show your work - Work alone
1. (a) A committee consisting of a president, a vice president, a secretary, and a treasurer is to be selec
Math319, Spring 2010
Quiz 1
Thursday, February 18, 2010 9.05 - 9.45am
Name :
No use of notes or textbook - Show your work - Work alone
1. Consider an experiment whose sample space is S . For each event E of the sample space S , we assume that a number P(E
Probability and Statistics Math319, Spring 2010 Project Presentation Comment Sheet March 16 & 18, 2010
Content: Was the presentation informative? Did it provide insight into the subject matter? Was it especially creative or well written? 4 (Excellent) 3
Math 319, Spring 2010
Midterm
Thursday, March 11, 2010 9.05 - 10.15 am
Name :
No use of notes or textbook - For full credit, show work and explain answers - Work alone
1. Consider an experiment whose sample space is S . For each event E of the sample spac
Probability and Statistics Math319, Spring 2010 Properties of the Cumulative Distribution Function April 15, 2010 Let X be a random variable with cumulative distribution function F . 1. F is a non-decreasing function. Proof. Let a, b R where a b.
Thus F (
Probability and Statistics Math319, Spring 2010 Axiom Jan 26 2010 What do you understand by the term axiom in math? Write a few sentences on your understanding of this term and on how it is used in math.
Look at the denition of vector space on the page yo