Statistics 451 Midterm October 11, 2013
This exam has 3 problems and is worth 40 points.
Instructor: Michael Kozdron
You have 50 minutes to complete this exam. Please read all instructions carefully,
Statistics 451 (Fall 2013)
Prof. Michael Kozdron
September 25, 2013
Lecture #10: Continuity of Probability
Recall that last class we proved the following theorem.
Theorem 10.1. Consider the real numbe
Statistics 451 (Fall 2013)
Prof. Michael Kozdron
September 27, 2013
Lecture #11: Continuity of Probability (continued)
We will now apply the continuity of probability theorem to prove that the functio
Statistics 451 (Fall 2013)
Prof. Michael Kozdron
September 11, 2013
Lecture #4: There is no uniform probability on ([0, 1], 2[0,1] )
Our goal for today is to prove the rst of the claims made last lect
Statistics 451 (Fall 2013)
Prof. Michael Kozdron
September 23, 2013
Lecture #9: Construction of a Probability (Part II)
Recall that we have been trying to construct a uniform probability on [0, 1]. As
Statistics 451 (Fall 2013)
Prof. Michael Kozdron
September 20, 2013
Lecture #8: Independence and Conditional Probability
Denition. Let (, F , P) be a probability space. The events A, B F are said to b
Statistics 451 (Fall 2013)
Prof. Michael Kozdron
September 16, 2013
Lecture #6: Construction of a Probability (Part I)
As we showed in Lecture #4, when the sample space is = [0, 1], it is not possible
Statistics 451 (Fall 2013)
Prof. Michael Kozdron
September 13, 2013
Lecture #5: The Borel Sets of R
We will now begin investigating the second of the two claims made at the end of Lecture #3,
namely t
Statistics 451 (Fall 2013)
Prof. Michael Kozdron
September 18, 2013
Lecture #7: Proof of the Monotone Class Theorem
Our goal for today is to prove the monotone class theorem. We will then deduce an ex
Stat 451: Solutions to Assignment #1
(2.1) By denition, 2 is the set of all subsets of . Therefore, to show that 2 is a -algebra we
must show that the conditions of the denition -algebra are met. In p
Stat 851: Solutions to Assignment #3
(7.11) To see that A is a Borel set write A as
A = cfw_x0 = cfw_(, x0 ) (x0 , )c .
()
Since open intervals are Borel, so too are unions of open intervals, as are
Stat 451: Solutions to Assignment #2
(3.1) If A B = , then by Theorem 2.2 we conclude P (A B ) = P () = 0. Hence, in order for A
and B to be independent, it must be the case that P (A B ) = P (A) P (B
Stat 451 Fall 2013
Assignment #2
This assignment is due on Monday, September 23, 2013.
1. Complete the following exercises from pages 1920.
#3.1, 3.3, 3.6, 3.8, 3.11, 3.12, 3.13
2. Complete the follo
Stat 451 Fall 2013
Assignment #3
This assignment is due on Friday, October 25, 2013.
1. Complete the following exercises from pages 4546.
#7.11, 7.12, 7.13, 7.14, 7.15, 7.17, 7.18
Stat 451 Fall 2013
Assignment #1
This assignment is due on Monday, September 16, 2013.
1. Complete the following exercises from pages 1213.
#2.1, 2.2, 2.3, 2.6, 2.9, 2.10, 2.11, 2.12, 2.14, 2.15, 2.1