“random variable”的概念、定义、翻译、参考文献-科学参考

random variable

Mathematics

A quantity that takes different numerical values according to the result of a particular experiment. For example, if a die is rolled, then the number rolled is a random variable on the sample space of possible rolls.

A random variable is discrete if the set of possible values is finite or denumerable. For a discrete random variable, the probability of its taking any particular value is given by the probability mass function.

A random variable is continuous if possible outcomes are distributed over uncountably many values and the cumulative distribution function F_X(x) = P(X ≤ x) is a continuous function. If F_X is piecewise differentiable, then the derivative f_X is the probability density function.

Some random variables are mixed in the sense of having both discrete and continuous characteristics. For example, in modelling the lifetime T of a light bulb, there may be a non-zero probability p of the light bulb blowing immediately (so T=0) and the remaining 1–p is distributed over T>0 continuously.

Formally, a random variable on a probability space Ω‎ is a measurable function X:Ω‎→ℝ.

Statistics

When the value of a variable is subject to random variation, or when it is the value of a randomly chosen member of a population, it is described as a random variable—though the adjective ‘random’ may be omitted. See probability distribution.

Computer

A quantity that may take any of a prescribed set of values with relative frequency determined by its probability distribution.

Philosophy

Intuitively, a variable, such as height, that can take various values in a population, and such that some values have some probability of occurrence, and others a different probability (for example, there might be a probability of one in ten that a person is 5′ 8′′ tall, but only one in a thousand that he or she is 6′ 8′′ tall). In probability theory a random variable is a variable X that can take any one of a finite or countably infinite range of values, each with a probability. The distribution of a random variable is the set of pairs (x_i, Prob X=x_i), giving the probability associated with each value in the range. In the example, (5′ 8′′, 0·1) would be one member of the distribution of the random variable of height in a population, if 10% of the population is that tall.

Economics

A function that maps the outcomes of a random experiment onto the real numbers. For example, one can define a random variable X as taking value 0 when a tossed coin shows ‘heads’ and value 1 when the coin shows ‘tails’. A random variable is characterized by a probability distribution, i.e. the set of all possible values that it can assume and the corresponding probabilities. A random variable is continuous, or has a continuous distribution, if it can take any values from an interval, bounded or unbounded; and it is discrete, or has a discrete distribution, if it can only take a countable, finite or infinite, number of values.

单词	random variable
释义	random variable Mathematics A quantity that takes different numerical values according to the result of a particular experiment. For example, if a die is rolled, then the number rolled is a random variable on the sample space of possible rolls. A random variable is discrete if the set of possible values is finite or denumerable. For a discrete random variable, the probability of its taking any particular value is given by the probability mass function. A random variable is continuous if possible outcomes are distributed over uncountably many values and the cumulative distribution function F_X(x) = P(X ≤ x) is a continuous function. If F_X is piecewise differentiable, then the derivative f_X is the probability density function. Some random variables are mixed in the sense of having both discrete and continuous characteristics. For example, in modelling the lifetime T of a light bulb, there may be a non-zero probability p of the light bulb blowing immediately (so T=0) and the remaining 1–p is distributed over T>0 continuously. Formally, a random variable on a probability space Ω‎ is a measurable function X:Ω‎→ℝ. Statistics When the value of a variable is subject to random variation, or when it is the value of a randomly chosen member of a population, it is described as a random variable—though the adjective ‘random’ may be omitted. See probability distribution. Computer A quantity that may take any of a prescribed set of values with relative frequency determined by its probability distribution. Philosophy Intuitively, a variable, such as height, that can take various values in a population, and such that some values have some probability of occurrence, and others a different probability (for example, there might be a probability of one in ten that a person is 5′ 8′′ tall, but only one in a thousand that he or she is 6′ 8′′ tall). In probability theory a random variable is a variable X that can take any one of a finite or countably infinite range of values, each with a probability. The distribution of a random variable is the set of pairs (x_i, Prob X=x_i), giving the probability associated with each value in the range. In the example, (5′ 8′′, 0·1) would be one member of the distribution of the random variable of height in a population, if 10% of the population is that tall. Economics A function that maps the outcomes of a random experiment onto the real numbers. For example, one can define a random variable X as taking value 0 when a tossed coin shows ‘heads’ and value 1 when the coin shows ‘tails’. A random variable is characterized by a probability distribution, i.e. the set of all possible values that it can assume and the corresponding probabilities. A random variable is continuous, or has a continuous distribution, if it can take any values from an interval, bounded or unbounded; and it is discrete, or has a discrete distribution, if it can only take a countable, finite or infinite, number of values.
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