Observable Random Variable
An Observable Random Variable is a random variable that is an observable variable.
- Example(s):
- a Statistic.
- See: Latent Random Variable, Statistical Parameter, Data Variable.
References
2015
- http://wikipedia.org/wiki/Statistic#Observability
- A statistic is an observable random variable, which differentiates it both from a parameter that is a generally unobservable quantity describing a property of a statistical population, and from an unobservable random variable, such as the difference between an observed measurement and a population average. A parameter can only be computed exactly if the entire population can be observed without error; for instance, in a perfect census or for a population of standardized test takers.
Statisticians often contemplate a parameterized family of probability distributions, any member of which could be the distribution of some measurable aspect of each member of a population, from which a sample is drawn randomly. For example, the parameter may be the average height of 25-year-old men in North America. The height of the members of a sample of 100 such men are measured; the average of those 100 numbers is a statistic. The average of the heights of all members of the population is not a statistic unless that has somehow also been ascertained (such as by measuring every member of the population). The average height of all (in the sense of genetically possible) 25-year-old North American men is a parameter, and not a statistic.
- A statistic is an observable random variable, which differentiates it both from a parameter that is a generally unobservable quantity describing a property of a statistical population, and from an unobservable random variable, such as the difference between an observed measurement and a population average. A parameter can only be computed exactly if the entire population can be observed without error; for instance, in a perfect census or for a population of standardized test takers.
2013
- http://www.math.uah.edu/stat/point/Likelihood.html
- QUOTE: Suppose again that we have an observable random variable [math]\displaystyle{ X }[/math] for an experiment, that takes values in a set S. Suppose also that distribution of [math]\displaystyle{ X }[/math] depends on an unknown parameter θ, taking values in a parameter space Θ. Specifically, we will denote the probability density function of [math]\displaystyle{ X }[/math] on S by [math]\displaystyle{ f_θ }[/math] for θ∈Θ. Of course, our data variable [math]\displaystyle{ X }[/math] will almost always be vector-valued. The parameter θ may also be vector-valued. … we try to find the values of the parameters that would have most likely produced the data we in fact observed. ...