Probability Theory (ePub)

Analysis theory of any random phenomena is known asprobability. Main resource for concept of probability isprobability theory. Probability theory is said to be one of manymost important concepts or branches of mathematics. Followingobjects are known as main concepts or central objects:Random variablesStochastic processesRandom eventsMeasured quantitiesEvents are a kind of abstraction achieved through mathematicalprocess. This abstraction is done on the base ofnon-deterministic events. Measured quantities can also be usedfor such abstraction. Measured quantities can be singleoccurrence or also follow random fashion for time evolvingmultiple occurrences. Making predictions about the outcome ofrandom events is not always easy or even impossiblesometimes. However, if influences are made on sequence ofindividual events, they will tend to follow certain patterns thatare much easy to study, practice and predict. For instance, ifoutcome of coin flipping or roll of dice is influenced by outerfactors such as friction, they will follow a specific pattern whenproving outcome. Once this certain pattern is figured out andunderstood properly, it becomes much easier to predict theoutcome with maximum accuracy. It means that it is hard tounderstand future outcome of subsequent random events thatmakes it hard to predict them. However, it is easy to predictpattern exhibited by these group of events that makes it easyto predict them and their corresponding events also. Todescribe such patterns certain mathematical results or conceptsare used. Law of large numbers and central limit theorem aretwo main concepts that are used to study and describe suchpatterns followed by sequential random events.Mathematical foundations of statistics consider probability theoryas a practical part for any human activity in which, quantitativeanalysis of large data sets are involved. Involving in dailyhuman activities makes probability theory a main concept ofmathematics and statistics. It is also heavily involved in manymathematical and statistical concepts, which also makes itimportant for one to learn and understand basic concepts ofthis theory. Probability theory can also be used to describecomplex systems, systems that hold only partial knowledge oftheir corresponding state. These descriptions are done the sameway they are done in statistical mechanics. This is the mainreason for which this theory is considered as a part of bothmathematics and statistics. However, mathematics and statisticsare parent theories for each other so any concept ofmathematics can be a concept of statistics and any concept ofstatistics can be a concept of mathematics. Discovery ofprobabilistic behavior of physical phenomena is considered agreat discovery in the field of physics. This probabilistic behaviorwas observed at atomic scales. This whole observation washeavily related to the concepts of probability theory. However,probability theory was not used as a complete base in thattheory. This concept and research is broadly described intheory of quantum mechanics. Quantum mechanics is arguablythe only field in physics, which is related with the concepts ofprobability theory. However, researches are still going on andmore connections are much likely to be found out soon thanksto the deep relations between mathematics and physics.