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Chapter 8
Section 8.1
Check Your Understanding, page 485:
1. We are 95% confident that the interval from 2.84 to 7.55 g captures the population standard
deviation of the fat content of Brand X
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Section 7.2
Check Your Understanding, page 445:
1. The mean of the sampling distribution of p is equal to the population proportion. In this case
p = p = 0.75.
2. The standard deviation of the sampl
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Chapter 7
Section 7.1
Check Your Understanding, page 425:
1. The parameter is = 20 ounces of iced tea. The statistic is x = 19.6 ounces of iced tea.
2. The parameter is p = 0.10, or 10% of passeng
AP STATISTICS CHAPTER 10 REVIEW
_1. You want to compute a 96% confidence interval for a population mean. Assume that =
10
and the sample size is 50. The value of z* to be used in this calculation is
(a) 1.960
(b) 1.645
(c) 1.7507
(d) 2.0537
_2. You want t
Week 6: Lp Spaces
Document prepared by Anna Rozanova-Pierrat1
1
Lecture 6.1: Introduction
1.1
Definitions
We have introduced Lp and Lploc -spaces in Week 2. In Week 3 we have proved that Lp for 1 p
is a Banach space (Fischer-Riesz Theorem).
Definition 1
Week 4: Hilbert spaces
Document prepared by Anna Rozanova-Pierrat1
1
Lecture 4.2: Bilinear forms
Definition 1 Let X be a vector space. We call bilinear form on X a function a : X X
such that, for all u, v, w in X and , in R , we have:
R
1. a(u + v, w) =
Polycopi du cours de la 3me anne, MOA
Analyse Fonctionnelle
A. Rozanova-Pierrat
17 september 2015
Contents
Introduction
v
1 Notations
1
2 Reminders on the topology in metric and normed spaces
2.1 Distance or metric . . . . . . . . . . . . . . . . . . . .
Week 3: Banach Spaces and Linear
Continuous Operators
Document prepared by Anna Rozanova-Pierrat
1
1
Lecture 3.2: Banach spaces
Definition 1 A normed vector space that is complete is called a Banach space.
Example 1
1.
Rn is a Banach space for any norm de
Week 5: Lax Milgram & Complements
on Hilbert spaces
Document prepared by Anna Rozanova-Pierrat1
1
Lecture 5.2: Continuity and coercivity of a bilinear form
We refer to Lectures 4.2, 4.3 and 4.6 for the definition of a bilinear form and its properties on a
Week 3
BANACH SPACES &
LINEAR CONTINUOUS
FUNCTIONS
Week 3
Lecture 3.1
INTRODUCTION
What we will learn this week:
What is a Banach space?
The Fischer-Riesz theorem
What is L(X,Y)?
What is a dual space?
What is the weak topology?
Strong vs. weak converge
Week 5
LAX MILGRAM & COMPLEMENTS
ON HILBERT SPACES
Week 5
Lecture 5.1
INTRODUCTION
What we will learn this week:
The Lax-Milgram Lemma
Strong and weak convergence in a Hilbert
Hilbertian Basis
Week 5
Lecture 5.2
CONTINUITY AND COERCIVITY OF
A BILINEAR
Week 6
LP SPACES
Week 6
Lecture 6.1
INTRODUCTION
Four weeks ago
For p [1,[, we defined Lp() the set of
measurable functions from to R
whose p-th power belongs to L1().
We defined L() the set of measurable functions
from to R for which there exists a real
Week 4
HILBERT SPACES
Week 4
Lecture 4.1
INTRODUCTION
What we will learn this week:
What is an inner product?
What is a Hilbert space?
The Riesz Representation Theorem
Who is the dual space of a Hilbert space?
How to define a linear operator with a b