Order ID 53563633773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages
Probability theory is a branch of mathematics concerned with the study of random phenomena. It is used to model uncertain events and to make predictions about the likelihood of different outcomes.
The basic idea of probability theory is to assign a number between 0 and 1, known as a probability, to each possible outcome of a random event. A probability of 0 means that the outcome is impossible, while a probability of 1 means that the outcome is certain. Probabilities between 0 and 1 represent degrees of uncertainty, with higher probabilities indicating greater likelihood.
Probability theory is used in a wide range of fields, including statistics, physics, engineering, economics, and finance. Some common applications of probability theory include:
- Risk assessment: Probability theory is used to assess the likelihood of different risks and to determine how to manage them. For example, insurance companies use probability theory to calculate the premiums they charge for different types of insurance policies.
- Statistical inference: Probability theory is used to make inferences about populations based on samples of data. For example, researchers might use probability theory to determine whether the results of a clinical trial are statistically significant.
- Random processes: Probability theory is used to model the behavior of random processes, such as the stock market or the weather. These models can be used to make predictions and to develop strategies for managing risk.
- Game theory: Probability theory is used in game theory to analyze strategic interactions between players. For example, economists might use probability theory to model the behavior of firms in a market.
- Artificial intelligence: Probability theory is used in artificial intelligence to model uncertainty and to make decisions based on incomplete information. For example, a self-driving car might use probability theory to determine the likelihood of different obstacles on the road.
There are several different types of probability, including:
- Classical probability: This type of probability is based on assumptions about the underlying probability distribution of the outcomes. For example, if we assume that a coin is fair, we can calculate the probability of getting heads or tails.
- Empirical probability: This type of probability is based on observations of the frequency of outcomes in a sample. For example, we might roll a die many times and observe the frequency of different outcomes.
- Subjective probability: This type of probability is based on personal beliefs or judgments about the likelihood of different outcomes. For example, a meteorologist might assign a subjective probability to the likelihood of rain based on their experience and knowledge of weather patterns.
Probability theory is a complex and highly mathematical field, with many different concepts and techniques. Some key concepts include:
- Conditional probability: This is the probability of one event occurring given that another event has occurred. For example, the probability of getting heads on a second coin flip given that the first flip was heads.
- Bayes’ theorem: This is a formula for calculating conditional probabilities. It is widely used in statistical inference and machine learning.
- Random variables: These are variables that take on different values with different probabilities. For example, the outcome of a coin flip is a random variable that can take on the values of heads or tails.
- Probability distributions: These are mathematical functions that describe the probabilities of different outcomes of a random variable. Common probability distributions include the normal distribution, the Poisson distribution, and the binomial distribution.
In conclusion, probability theory is a powerful tool for modeling and understanding uncertain events. It has many practical applications in fields ranging from finance to artificial intelligence. While it is a complex and highly mathematical field, understanding the basic concepts of probability theory can be extremely valuable in many areas of life.
QUALITY OF RESPONSE NO RESPONSE POOR / UNSATISFACTORY SATISFACTORY GOOD EXCELLENT Content (worth a maximum of 50% of the total points) Zero points: Student failed to submit the final paper. 20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. 30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. 40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. 50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. Use of Sources (worth a maximum of 20% of the total points). Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. 5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. 10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. 15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6th Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources. 20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment. Grammar (worth maximum of 20% of total points) Zero points: Student failed to submit the final paper. 5 points out of 20: The paper does not communicate ideas/points clearly due to inappropriate use of terminology and vague language; thoughts and sentences are disjointed or incomprehensible; organization lacking; and/or numerous grammatical, spelling/punctuation errors 10 points out 20: The paper is often unclear and difficult to follow due to some inappropriate terminology and/or vague language; ideas may be fragmented, wandering and/or repetitive; poor organization; and/or some grammatical, spelling, punctuation errors 15 points out of 20: The paper is mostly clear as a result of appropriate use of terminology and minimal vagueness; no tangents and no repetition; fairly good organization; almost perfect grammar, spelling, punctuation, and word usage. 20 points: The paper is clear, concise, and a pleasure to read as a result of appropriate and precise use of terminology; total coherence of thoughts and presentation and logical organization; and the essay is error free. Structure of the Paper (worth 10% of total points) Zero points: Student failed to submit the final paper. 3 points out of 10: Student needs to develop better formatting skills. The paper omits significant structural elements required for and APA 6th edition paper. Formatting of the paper has major flaws. The paper does not conform to APA 6th edition requirements whatsoever. 5 points out of 10: Appearance of final paper demonstrates the student’s limited ability to format the paper. There are significant errors in formatting and/or the total omission of major components of an APA 6th edition paper. They can include the omission of the cover page, abstract, and page numbers. Additionally the page has major formatting issues with spacing or paragraph formation. Font size might not conform to size requirements. The student also significantly writes too large or too short of and paper 7 points out of 10: Research paper presents an above-average use of formatting skills. The paper has slight errors within the paper. This can include small errors or omissions with the cover page, abstract, page number, and headers. There could be also slight formatting issues with the document spacing or the font Additionally the paper might slightly exceed or undershoot the specific number of required written pages for the assignment. 10 points: Student provides a high-caliber, formatted paper. This includes an APA 6th edition cover page, abstract, page number, headers and is double spaced in 12’ Times Roman Font. Additionally, the paper conforms to the specific number of required written pages and neither goes over or under the specified length of the paper.
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