Probability Concepts and Applications

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Table of Contents

Rationale
Types of Probability
Probability Distributions
A Normal Distribution
Understanding Distribution
References

Rationale

The utilization of probability concepts is a manner of articulating knowledge or conviction that an incident will happen or has taken place (Anderson, Sweeney, Williams, Camm, & Cochran, 2013). Such concepts have been offered a precise mathematical significance in the probability theory, which is employed broadly in fields such as statistics, management, mathematics, and science to present determinations regarding the possibility of likely occurrences and the fundamental mechanics of intricate schemes.

Types of Probability

There are four kinds of probability. No type of probability is incorrect though some are deemed more practical when judged against the others (Chen, Geng, & Zhi-Ming, 2011). The first type is the classical probability, which attributes probabilities in the lack of any substantiation, or in the existence of a symmetrically reasonable proof.

The classical theory of probability relates to similarly likely occurrences, which are referred to as equipossible. The second type of probability is the logical probability, which maintains the notion of the classical understanding that possibilities could be established theoretically through an assessment of the extent of options.

The third type is the subjective probability, which is founded on a person’s decision regarding the likelihood of the occurrence of a given result. Subjective probability holds no official computations and just reveals the perspectives of the subject and past encounters.

The fourth type is the physical probability, which is also referred to as the objective probability; it is related to random physical structures, for instance, wheels. In such structures, a specific kind of occurrence has a tendency of happening at an unrelenting speed, or relative occurrence, in a lengthy run of attempts.

This kind of probability either elucidates, or is called upon to enlighten, the stable rates of occurrence (Jiang, Pei, Tao, & Lin, 2013). On this note, the application of physical probability is just sensible when handling well identified random trials.

Probability Distributions

The effectiveness of probability theory occurs in the comprehension of probability distributions (also referred to as probability functions) (Devore, 2015). Probability distributions portray or depict probabilities for every achievable incidence of a random variable. There are a couple of probability distributions, which encompass the discrete distributions or continuous distributions.

Discrete probability distributions express a fixed set of achievable incidences, for distinct count data. For instance, the number of triumphant business undertakings out of 2 is distinct since the chance variable signifies the level of the activities that succeeded, which could only be 0, 1, or 2. On the other hand, continuous probability distributions define an unbroken range of likely incidences.

For instance, the adequate capital for a given business could be anything from about 500 dollars to over a million dollars. In this regard, the random variable of adequate capital is continuous, with an unlimited number of possible values between any two amounts (Eisinga, Breitling, & Heskes, 2013). There are numerous different categories of continuous and discrete probability distributions.

A Normal Distribution

A normal distribution denotes a generally continuous probability distribution, which is significant in statistics and is normally employed to determine actual-valued random variables with unidentified distributions. Therefore, a normal distribution plots the values in a proportionate style and the majority of the outcomes are positioned about the mean (Csörgo & Révész, 2014).

Understanding Distribution

Business projects are filled with uncertainties, which could be portrayed by a figure of an indeterminate random value (Eisinga et al., 2013). Nevertheless, the comprehension of probability distribution could assist business managers in the quantification of variables with the purpose of realizing the most favorable decisions for the project, for example, the number of personnel that could be hired to ensure the triumph of a business project.

References

Anderson, D., Sweeney, D., Williams, T., Camm, J., & Cochran, J. (2013). Statistics for business & economics. Boston, Massachusetts: Cengage Learning.

Chen, D., Geng, Z., & Zhi-Ming, M. (2011). Probability and statistics. Frontiers of Mathematics in China, 6(6), 1021-1024.

Csörgo, M., & Révész, P. (2014). Strong approximations in probability and statistics. Waltham: Academic Press.

Devore, J. (2015). Probability and statistics for engineering and the sciences. Boston, Massachusetts: Cengage Learning.

Eisinga, R., Breitling, R., & Heskes, T. (2013). The exact probability distribution of the rank product statistics for replicated experiments. FEBS Letters, 587(6), 677-682.

Jiang, B., Pei, J., Tao, Y., & Lin, X. (2013). Clustering uncertain data based on probability distribution similarity. Knowledge and Data Engineering, IEEE Transactions on, 25(4), 751-763.

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