# 1.2 Interpretations  (Page 2/5)

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There is a variety of points of view as to how probability should be interpreted. These impact the manner in which probabilities are assigned(or assumed). One important dichotomy among practitioners.

• One group believes probability is objective in the sense that it is something inherent in the nature of things. It is to be discovered, if possible, by analysisand experiment. Whether we can determine it or not, “it is there.”
• Another group insists that probability is a condition of the mind of the person making the probability assessment. From this point of view, the laws of probability simply impose rational consistency upon the way one assigns probabilities to events. Various attempts have been made to find objectiveways to measure the strength of one's belief or degree of certainty that an event will occur. The probability $P\left(A\right)$ expresses the degree of certainty one feels that event A will occur. One approach to characterizing an individual's degree of certainty is toequate his assessment of $P\left(A\right)$ with the amount a he is willing to pay to play a game which returns one unit of money if A occurs, for a gain of $\left(1-a\right)$ , and returns zero if A does not occur, for a gain of $-a$ . Behind this formulation is the notion of a fair game , in which the “expected” or “average” gain is zero.

The early work on probability began with a study of relative frequencies of occurrence of an event under repeated but independent trials. This idea is so imbedded in much intuitive thought about probability that some probabilistshave insisted that it must be built into the definition of probability. This approach has not been entirely successful mathematically and has notattracted much of a following among either theoretical or applied probabilists. In the model we adopt, there is a fundamental limit theorem, known as Borel's theorem , which may be interpreted “if a trial is performed a large number of times in anindependent manner, the fraction of times that event A occurs approaches as a limit the value $P\left(A\right)$ . Establishing this result (which we do not do in this treatment) provides a formal validation of the intuitive notion that lay behindthe early attempts to formulate probabilities. Inveterate gamblers had noted long-run statistical regularities, and sought explanations from their mathematically giftedfriends. From this point of view, probability is meaningful only in repeatable situations. Those who hold this view usually assume an objective view of probability. It is a numberdetermined by the nature of reality, to be discovered by repeated experiment.

There are many applications of probability in which the relative frequency point of view is not feasible. Examples include predictions of the weather, the outcome of agame or a horse race, the performance of an individual on a particular job, the success of a newly designed computer. These are unique, nonrepeatable trials. As the popularexpression has it, “You only go around once.” Sometimes, probabilities in these situations may be quite subjective. As a matter of fact, those who take asubjective view tend to think in terms of such problems, whereas those who take an objective view usually emphasize the frequency interpretation.

what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
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A fair die is tossed 180 times. Find the probability P that the face 6 will appear between 29 and 32 times inclusive