Vorbereitung zur Mathematik fr VWL und Statistik
Reinhard Ullrich Version 30.09.2010
Basierend auf: H. Schichl, R. Steinbauer,
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Inhaltsverzeichnis
1 Einleitung
Einfhrung in das mathematische
,
Homework 2 Solutions
Math 171, Spring 2010
Please send corrections to [email protected]
9.6. Prove that if A and B are countable sets, then A B is countable.
Solution. For a fixed a A, let Ba =
Homework 3 Solutions
Math 171, Spring 2010
Please send corrections to [email protected]
17.4. Let cfw_an be a sequence with positive terms such that limn an = L > 0. Let x be a real number.
Pr
6
Completeness
6.1
Cauchy sequences
Definition 6.1. A sequence (xn ) of elements of a metric space (X, %) is
called a Cauchy sequence if, given any > 0, there exists N such that
%(xn , xm ) < for all
1
Chapter 10: Compact Metric Spaces
10.1 Definition. A collection of open sets cfw_Ui : i I in X is an open
cover of Y X if Y iI Ui . A subcover of cfw_Ui : i I is a subcollection
cfw_Uj : j J for som
1.4. DISTRIBUTION FUNCTIONS
9
1.4 Distribution Functions
Definition 1.8. The probability of the event (X x) expressed as a function of
x R:
FX (x) = PX (X x)
is called the cumulative distribution func
Homework 4 Solutions
Math 171, Spring 2010
Please send corrections to [email protected]
P p
P
P
26.5. Let n=1 an and n=1 bn be absolutely convergent series. Prove that the series n=1 |an bn |
c
Chapter 3
Random Variables and
Measurable Functions.
3.1
Measurability
Definition 42 (Measurable function) Let f be a function from a measurable
space (, F) into the real numbers. We say that the func