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Lecture

Estimating Random Variables

Description

This lecture covers the estimation of random variables, including functions of discrete random variables, calculation of expected values, and properties of probability distributions. It also discusses the relationship between random variables and their functions, with examples illustrating the concepts presented.

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Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (22)

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.

Independent and identically distributed random variables

In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as i.i.d., iid, or IID. IID was first defined in statistics and finds application in different fields such as data mining and signal processing. Statistics commonly deals with random samples. A random sample can be thought of as a set of objects that are chosen randomly.

Convergence of random variables

In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied.

Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.

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.

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