Analysis theory of any random phenomena is known as
probability. Main resource for concept of probability is
probability theory. Probability theory is said to be one of many
most important concepts or branches of mathematics. Following
objects are known as main concepts or central objects:
Random variables
Stochastic processes
Random events
Measured quantities
Events are a kind of abstraction achieved through mathematical
process. This abstraction is done on the base of
non-deterministic events. Measured quantities can also be used
for such abstraction. Measured quantities can be single
occurrence or also follow random fashion for time evolving
multiple occurrences. Making predictions about the outcome of
random events is not always easy or even impossible
sometimes. However, if influences are made on sequence of
individual events, they will tend to follow certain patterns that
are much easy to study, practice and predict. For instance, if
outcome of coin flipping or roll of dice is influenced by outer
factors such as friction, they will follow a specific pattern when
proving outcome. Once this certain pattern is figured out and
understood properly, it becomes much easier to predict the
outcome with maximum accuracy. It means that it is hard to
understand future outcome of subsequent random events that
makes it hard to predict them. However, it is easy to predict
pattern exhibited by these group of events that makes it easy
to predict them and their corresponding events also. To
describe such patterns certain mathematical results or concepts
are used. Law of large numbers and central limit theorem are
two main concepts that are used to study and describe such
patterns followed by sequential random events.
Mathematical foundations of statistics consider probability theory
as a practical part for any human activity in which, quantitative
analysis of large data sets are involved. Involving in daily
human activities makes probability theory a main concept of
mathematics and statistics. It is also heavily involved in many
mathematical and statistical concepts, which also makes it
important for one to learn and understand basic concepts of
this theory. Probability theory can also be used to describe
complex systems, systems that hold only partial knowledge of
their corresponding state. These descriptions are done the same
way they are done in statistical mechanics. This is the main
reason for which this theory is considered as a part of both
mathematics and statistics. However, mathematics and statistics
are parent theories for each other so any concept of
mathematics can be a concept of statistics and any concept of
statistics can be a concept of mathematics. Discovery of
probabilistic behavior of physical phenomena is considered a
great discovery in the field of physics. This probabilistic behavior
was observed at atomic scales. This whole observation was
heavily related to the concepts of probability theory. However,
probability theory was not used as a complete base in that
theory. This concept and research is broadly described in
theory of quantum mechanics. Quantum mechanics is arguably
the only field in physics, which is related with the concepts of
probability theory. However, researches are still going on and
more connections are much likely to be found out soon thanks
to the deep relations between mathematics and physics.
Título : Probability Theory
EAN : 9781393417699
Editorial : IntroBooks
El libro electrónico Probability Theory está en formato ePub
¿Quieres leer en un eReader de otra marca? Sigue nuestra guía.
Puede que no esté disponible para la venta en tu país, sino sólo para la venta desde una cuenta en Francia.
Si la redirección no se produce automáticamente, haz clic en este enlace.
Conectarme
Mi cuenta