Lecture

Probability Theory: Events and Tribes

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Description

This lecture introduces the concept of events and tribes in probability theory. It covers the definition of an event space, the properties of events in a tribe, and the importance of defining valid tribes. The lecture also discusses examples of different tribes based on observable outcomes, emphasizing the role of tribes in modeling random experiments. Furthermore, it explores the significance of choosing appropriate tribes based on the sample space and the events of interest. The lecture concludes with practical applications of tribes in defining probabilities and establishing relationships between different events.

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Mathematics

Probability theory: Topics in probability theory

Related concepts (29)

Probability space

In probability theory, a probability space or a probability triple is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a die. A probability space consists of three elements: A sample space, , which is the set of all possible outcomes. An event space, which is a set of events, , an event being a set of outcomes in the sample space. A probability function, , which assigns each event in the event space a probability, which is a number between 0 and 1.

Age of consent

The age of consent is the age at which a person is considered to be legally competent to consent to sexual acts. Consequently, an adult who engages in sexual activity with a person younger than the age of consent is unable to legally claim that the sexual activity was consensual, and such sexual activity may be considered child sexual abuse or statutory rape. The person below the minimum age is considered the victim, and their sex partner the offender, although some jurisdictions provide exceptions through "Romeo and Juliet laws" if one or both participants are underage, and are close in age.

Age of majority

The age of majority is the threshold of legal adulthood as recognized or declared in law. It is the moment when a person ceases to be considered a minor and assumes legal control over their person, actions, and decisions, thus terminating the control and legal responsibilities of their parents or guardian over them. Most countries set the age of majority at 18, but some jurisdictions have a higher age and others lower. The word majority here refers to having greater years and being of full age as opposed to minority, the state of being a minor.

Marriageable age

Marriageable age (or marriage age) is the general age, as a legal age or as the minimum age subject to parental, religious or other forms of social approval, at which a person is legitimately allowed for marriage. Age and other prerequisites to marriage vary between jurisdictions, but in the vast majority of jurisdictions, the marriage age as a right is set at the age of majority. Nevertheless, most jurisdictions allow marriage at a younger age with parental or judicial approval, especially if the female is pregnant.

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.

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