Solutions of HW4
1. Since A B, we have
P (AB)
P (A)
=
.
P (B)
P (B)
P (A|B) =
(1)
Let D1 , D2 denote the two outcomes. Then, B = cfw_D1 + D2 9 and
A = cfw_D1 + D2 = 10. Hence
P (A) =
=
=
6
X
i=1
6
X
i
Practice exam for Midterm 1 (50 minutes)
SUBMITTED BY :
PUID#:
CLASS SECTION: 165, 166
Remarks:
(i) NO calculators, books or notes are allowed on this exam. Turn off all
electronic devices.
(ii) This
Name
Student ID #
Instructor:
Sergey Kirshner
STAT 416 Spring 2012
Practice Exam #2
March 20, 2012
You are not allowed to use books or notes. Non-programmable non-graphing calculators
are permitted. P
Version: January 10, 2011. Check web page for any updates.
Desire and Determination Bring Any Goal Within Reach Math 416 / Stat 416: Probability Spring 2011 Division 1 MWF 11:30am - 12:20pm (REC 121)
1
Probability and conditional probability
1.1
Axioms of probability and its consequence
Basic Questions :
1. What is a sample space? What is an event?
2. What is a probability? What are the three axio
1
Probability and conditional probability
1.1
Axioms of probability and its consequence
Basic Questions :
1. What is a sample space? What is an event?
2. What is a probability? What are the three axio
MA416
Homework 1
Due Jan 31 2014
(Show your steps to get partial credits!)
1. List the elements of the following sets:
(a) cfw_x| x is a real number such that x2 = 1.
(b) cfw_x| x is an integer such t
Examples for Chapter 5 Bayes theorem
1. Suppose an individual applying to a college determines that he has an 80% chance of
being accepted and he knows that dormitory housing will only be provided for
Examples for independent events
1. An oil exploration company currently has two active projects, one in Asia and the other
is Europe. Let A be the event that the Asian project is successful and B the
Homework 8 (Due 04/10/2015)
Please show your detailed mathematical argument. Answers without
work will receive 0 point. You are allowed to submit your homework with a
partner. Staple your work if you
MA416
Homework 2
Due Feb.21 2014
(Show your steps to get partial credits!)
1. Let A denote the event student is female and let B denote the event student is
French. In a class of 100 students suppose
MA416
Homework 2
Due Feb.21 2014
(Show your steps to get partial credits!)
1. Let A denote the event student is female and let B denote the event student is
French. In a class of 100 students suppose
MA416
Homework 3
Due Mar.14 2014
(Show your steps to get partial credits!)
Part I: chapter 6, 7 and 8
1. Determine whether the random variable is discrete or continuous.
(i) Time between oil changes o
CHAPTER 2. SOME FUNDAMENTAL CONCEPTS
2.1 Sample Space
2.2 Set Properties; Identication of Events with Sets
2.3 Random Variables
2.4 Counting Results
2.1 Sample Space
Denition: A Sample space is sim
Solution of HW10
All problems are from Pages 62-63 of Rick Durretts book Essentials of
Stochastic Processes.
1.9(c) (Announced on Monday by email) Recall that there is a typo here: the
(2, 1)-entry sh
Remark: A typo in HW10: In Problem 1.9(c), the (2, 1)-entry should
be changed to 0.4. That is, the matrix should be
1
1 .6
2 .4
3 0
2
.4
.4
.2
3
0
.2 .
.8
Solution of HW9
All problems are from Pages 6
STAT/MA 41600
In-Class Problem Set #8: September 8, 2017
Solutions by Mark Daniel Ward
Problem Set 8 Answers
1. We have
(3)(6)
(31)(64)
P (X = 0) = 0 9 5 = (1)(6)
=
1/21,
P
(X
=
1)
=
= (3)(15)
126
126
STAT/MA 41600
In-Class Problem Set #9: September 11, 2017
Solutions by Mark Daniel Ward
Problem Set 9 Answers
n1 (1/6)(1/2)n1 (1/2) =
1. The probability that Leo takes n rolls and Melissa
Ptakes n rol
STAT/MA 41600
In-Class Problem Set #15: September 20, 2017
Solutions by Mark Daniel Ward
Problem Set 15 Answers
1. The probability that X is an even integer is 60 (1/3)0 (2/3)6 + 62 (1/3)2 (2/3)4 + 64
STAT/MA 41600
In-Class Problem Set #10: September 13, 2017
Solutions by Mark Daniel Ward
Problem Set 10 Answers
1a. The probability mass function of X is: pX (2) = 1/24, pX (3) = 2/24, pX (4) = 3/24,
STAT/MA 41600
In-Class Problem Set #7: September 6, 2017
Solutions by Mark Daniel Ward
Problem Set 7 Answers
1. The number of raindrops is a nonnegative integer, so X is a discrete random variable. Th