Abstract Random Experiment

An Abstract Random Experiment is a stable repeatable observable stochastic process that produces outcomes from a predefined sample space.

References

2011

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Experiment_%28probability_theory%29
• QUOTE: An experiment is any procedure that can be infinitely repeated and has a well defined set of outcomes. Examples include tossing a coin or rolling a die. In probability theory, an experiment refers to random experiment. An experiment is said to be random experiment if it has more than one possible outcomes. If an experiment has only one possible outcome then it is known as deterministic experiment. An experiment is composed of one or more trials. A trial with two mutually exclusive outcomes is known as Bernoulli trial.

• (Forbes et al., 2011) ⇒ Forbes, C., Evans, M., Hastings, N., & Peacock, B. (2011). Statistical distributions. John Wiley & Sons.
• A probabilistic experiment is some occurrence such as the tossing of coins, rolling dice or observation of rainfall on a particular day where a complex natural background leads to a chance outcome.

2009

• http://alea.ine.pt/english/html/glossar/html/glossar.html
• QUOTE: Random experiment: An experiment with the following characteristics: it can be repeatedly performed, in the same circumstances or in an independent manner, any time it is repeated; - the possible results are known; there is insufficient knowledge to know which result will be obtained from amongst the possible results when the experiment is performed or phenomenon observed.

1987

• (Hogg & Ledolter, 1987) ⇒ Robert V. Hogg and Johannes Ledolter. (1987). “Engineering Statistics. Macmillan Publishing Company.
• Random experiments have outcomes that cannot be determined with certainty before the experiments are performed... The collection of all possible outcomes, namely [math]S[/math] = {H,T}, is called the sample space. Suppose that we are interested in a subset [math]A[/math] of our sample space; for example, in our case, let A={H} represent heads. Repeat this random experiment a number of times, say [math]n[/math], and count the number of times, say [math]f[/math], that the experiment ended in A. Here [math]f[/math] is called the frequency of the event A and the ratio f/n is called the relative frequency of the event [math]A[/math] in the [math]n[/math] trials of the experiment.

1986

• (Larsen & Marx, 1986) ⇒ Richard J. Larsen, and Morris L. Marx. (1986). “An Introduction to Mathematical Statistics and Its Applications, 2nd edition." Prentice Hall
• By an experiment we will mean any procedure that (1) can be repeated, theoretically, an infinite number of times; and (2) has a well-defined set of possible outcomes. Thus, rolling a pair of dice qualifies as an experiment; so does measuring a hypertensive's blood pressure or doing a stereographic analysis to determine the carbon content of moon rocks. Each of the potential eventualities of an experiment is referred to as a sample outcome, [math]s[/math], and their totality is called the sample space, S. To signify the member of [math]s[/math] in [math]S[/math], we write [math]s[/math] In S. Any designated collection of sample outcomes, including individual outcomes, the entire sample space, and the null set, constitutes an event. The latter is said to occur if the outcome of the experiment is one of the members of that event.