Which of the following describes the difference between overlapping and with

Disjoint events and independent events are different. Events are considered disjoint if they never occur at the same time; these are also known as mutually exclusive events. Events are considered independent if they are unrelated.

Disjoint Events Section

Disjoint events are events that never occur at the same time. These are also known as mutually exclusive events. 

These are often visually represented by a Venn diagram, such as the below. In this diagram, there is no overlap between event A and event B. These two events never occur together, so they are disjoint events.

Mutually Exclusive

Example: First-Year & Sophomore Students Section

Let's consider undergraduate class level. A student can be classified as a first-year student, sophomore, junior, or senior.

Being a first-year student and being a sophomore are disjoint events because an individual cannot be classified as both at the same time. 

Independent Events Section

Independent events are unrelated events. The outcome of one event does not impact the outcome of the other event. Independent events can, and do often, occur together. 

The following examples use stacked bar charts to demonstrated what two variables that are and are not independent look like in relation to one another. 

Example: Penguin Species & Biological Sex Section

MaleFemaleSegmented Bar ChartPenguin Sex by Species501001502000AdelieChinstrapGentooSpeciesFrequency

The segmented bar chart above displays data from a research study concerning penguins (see Palmer Penguins). Within each of the three species of penguin, half of the penguins are male and half are female. In this sample, penguin species and biological sex are independent. Knowing the species of a penguin does not change the probability that they are male or female. And, knowing the biological sex of a penguin does not change the probability that it is an Adelie, Chinstrap, or Gentoo penguin.

Non-Example: Enrollment Status by Campus Section

Full-TimePart-TimeStacked Bar ChartPenn State Enrollment Status by Campus010000 20000300004000050000University ParkCommonwealthCampusesPA College ofTechnologyWorld Campus

The segmented bar chart above displays data concerning Penn State students' status as full- or part-time and their primary campus (data from Penn State's Data Digest). The proportion of students who are part-time is different at each campus. Only 2.7% of University Park students are enrolled part-time while 69.2% of World Campus students are enrolled part-time. Enrollment status and primary campus are not independent. If we know a student's campus, that changes the probability of them being a full- or part-time student. If we know that a student is full- or part-time, that chances the probability that they came from a specific campus. 

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Describing differences between overlapping databases

Mathematisch-Naturwissenschaftliche Fakultät II

Die Analyse existierender Daten ist wichtiger Bestandteil moderner Forschung. Das Thema Datenqualität gewinnt deshalb im Bereich der wissenschaftlichen Forschung zunehmend an Bedeutung. Existierende Verfahren zur Datenbereinigung sind für wissenschaftliche Daten jedoch nur bedingt einsetzbar. Dies liegt zum einen an der höheren Komplexität der Daten und zum anderen an unserer oftmals noch unvollständigen Kenntnis der Regularien in den entsprechenden Domänen. Die vorliegende Arbeit ist leistet folgende Beiträge im Hinblick auf Datenqualität und Datenbereinigung wissenschaftlicher Daten: Im ersten Teil der Arbeit geben wir einen Überblick über existierende Verfahren zur Datenbereinigung und diskutieren deren Stärken und Schwächen. Aus unseren Ergebnissen folgern wir, daß überlappende Datenquellen großes Potential zur Verbesserung der Korrektheit und Genauigkeit wissenschaftlicher Daten haben. Überlappende Datenquellen decken Bereiche potentiell minderer Datenqualität in Form von (Daten-)konflikten auf und bieten gleichzeitig eine Möglichkeit zur Qualitätsverbesserung durch Datenintegration. Eine wichtige Voraussetzung für die Integration überlappender Datenquellen ist das Auflösen existierender Konflikte. In vielen Fällen treten die Konflikte nicht zufällig auf sondern folgen einer systematischen Ursache. Im zweiten Teil dieser Arbeit entwickeln wir Algorithmen, die das Auffinden systematischer Konflikte unterstützen. Wir klassifizieren Konflikte dabei anhand charakteristischer Muster in den überlappenden Daten. Diese Widerspruchsmuster unterstützen einen Experten bei der Festlegung von Konfliktlösungsstrategien zur der Datenintegration. Im dritten Teil dieser Arbeit verwenden wir ein prozeßbezogenes Model zur Beschreibung systematischer Konflikte, um Abhängigkeiten zwischen Konfliktgruppen aufzeigen zu können. Wir verwenden hierzu Sequenzen mengenorientierter Modifikationsoperationen die eine Datenquelle in die andere überführen. Wir präsentieren Algorithmen zur Bestimmung minimaler Modifikationssequenzen für ein gegebenes Paar von Datenquellen. Die Komplexität des Problems bedingt die Verwendung von Heuristiken. In unseren Experimenten zeigen wir die vielversprechende Qualität der Ergebnisse unserer Heuristiken.

Data quality has become an issue in scientific research. Cleaning scientific data, however, is hampered by incomplete or fuzzy knowledge of regularities in the examined domain. A common approach to enhance the overall quality of scientific data is to merge overlapping sources by eliminating conflicts that exist between them. The main objective of this thesis is to provide methods to aid the developer of an integrated system over contradicting databases in the task of resolving value conflicts. We contribute by developing a set of algorithms to identify regularities in overlapping databases that occur in conjunction with conflicts between them. These regularities highlight systematic differences between the databases. Evaluated by an expert user the discovered regularities provide insights on possible conflict reasons and help assess the quality of inconsistent values. Instead of inspecting individual conflicts, the expert user is now enabled to specify a conflict resolution strategy based on known groups of conflicts that share the same conflict reason. The thesis has three main parts. Part I gives a comprehensive review of existing data cleansing methods. We show why existing data cleansing techniques fall short for the domain of genome data and argue that merging overlapping data has outstanding ability to increase data accuracy; a quality criteria ignored by most of the existing cleansing approaches. Part II introduces the concept of contradiction patterns. We present a model for systematic conflicts and describe algorithms for efficiently detecting patterns that summarize characteristic data properties for conflict occurrence. These patterns help in providing answers to questions like “Which are the conflict-causing attributes, or values?” and “What kind of dependencies exists between the occurrences of contradictions in different attributes?”. In Part III, we define a model for systematic conflicts based on sequences of set-oriented update operations. Even though we only consider a restricted form of updates, our algorithms for computing minimal update sequences for pairs of databases require exponential space and time. We show that the problem is NP-hard for a restricted set of operations. However, we also present heuristics that lead to convincing results in all examples we considered.

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