Mathematics: Probability

Given a specific occasion or circumstance (for occurrence, redistribution of state use absolutely), what is the probability of a specific other occasion or response (eg. threatening vibe from an arbitrary individual from the people)? Altogether, we are tending to just the glorified inquiry of connections between's reflections that are illustrative of genuine ideas or objects, and totally disregarding the impact of elements other than those under study. It is vital to welcome the probabilistic quintessence of this "truth". It doesn't discuss what is out there, or what will really happen in specific situations, yet just of their relative probability, all different variables staying steady.

For this media assignment, I chose to focus on probability and the ways people don’t deal with it properly and probability based statements. In the text and in class we discussed gambler’s fallacy. First off, a fallacy is an incorrect argument in logic or a false belief based on an unsound argument. Gambler’s fallacy is a mistaken belief that if something happens less than it should in a normal period of time then it will happen more frequently in the future and same for if something happens more in a normal period of time then it will happen less in the future. This is where people act like the events are dependent but really, they are independent of each other. This can be a common thought in gambling.

‘Probability’ is a term used in mathematical situations and in normal social interactions. When there is a six sided die, what is the probability of it landing on any number below four? What events throughout the world had to happen in order for me to be born? Or most importantly to any gambler, what are the chances that I will win money on this bet? In the book The Drunkard’s Walk, the author Leonard Mlodinow addresses all of these questions in different sections of his book. This book’s style is very comforting as it led the reader through each topic so there is little confusion. This book helped me to understand that I do have control in what I do in life but surrounding each decision are multiple factors. Therefore, I should be mindful

Answer: the exponential distribution is used to model data with a continual failure rate. Also, it could be used to when questions needed to be answered, such as how much time will elapse before the earthquake occurs in a given region. How long do we need to wait before a customer enters a shop, and so on and so forth? (Wikipedia, n.d.)

Lorraine Daston discusses this in her 1995 book, Classical Probability in the Enlightenment. She focuses heavily on Bernoulli and how he redefined the art of conjecture. Conjecture as we knew it from the days of Ptolemy and Cicero was very qualitative and implausible, yet still serving a central purpose in society. However, “Bernoulli’s eighteenth-century followers set about transforming the art of conjecture into a calculus of probabilities.” Bernoulli recognized that risk and uncertainty are aspects of life that have always existed, and we must find rules to guide us in different situations of risk and doubt. Pierre Simon Laplace described what Bernoulli and others in the Enlightenment period were trying to do by coining the phrase: “Good sense reduced to a calculus.” Bernoulli proposes many equations and outlines lists of general rules to follow when it comes to forecasting. For instance, he says that “probabilities are estimated by the number of and the weight of proofs, proofs which in any way ascertain or show that some things exist, will exist, or have existed.” He goes on to talk about how we must not focus on the value of human actions in terms of their outcome, but on the process by which that outcome is achieved. Bernoulli believes that we must do this because foolish actions can lead to success and intelligent actions may lead to failure.

Probability is the final strand of the Australian curriculum relating to mathematics. Students using probability are “experimenting various theoretical approaches”- Australian Curriculum (2016). Probability is when you divide the number of outcomes in which an event can occur by the number of possible outcomes (Lakin, 2010, p.p131).

The foundation of the theory was the result of early work by Gerolamo Cardano, who in the 16th Century developed a method of computing chances in dice and cards by counting the equal probability of the outcomes (Mastin). Pascal and Fermat focused on two problems, one, which determined the chances of winning for each two men playing a particular dice game with specific rules, and determining how a game’s winnings should be divided between two equally skilled players if the game ended prematurely

Two scientists at the University of Iowa conducted an experiment in which research subjects played a game of chance with four separate card decks and stacks of play money. Each card told the person if they won or lost money. What the players did not know though was that the decks were

When discussing probability, a text of my previous reading came to mind. Within the lecture Physics II, much of Aristotle’s work is concerned with providing a definition for various events and subjects, and as such, identifying the types of causes for each event is an important step in accomplishing this goal. Aristotle specifically investigates the role of luck and chance as causes of change. Although we commonly speak of luck or chance as being a cause, Aristotle purposefully refrains from including them in his explanation of causes. When giving an account of our observable world, I agree with Aristotle in that there is no place for luck and chance as causes of events, yet I believe they do have a role, namely in predicting future events.

Prediction involves making a statement concerning the likely value of an event or action uncertain or unknown at the time of the statement. Since the theory of probability, (inaugurated by the French mathematicians Blaise Pascal and Pierre Fermat in 1654), was developed to quantify uncertain events in terms of their likelihood of occurrence, formal prediction is now viewed as a mathematical topic involving probabilistic modeling. Indeed, the mathematician Karl Pearson said in 1907 that the fundamental problem in statistics is prediction. Prediction, however, is usually not an end goal itself, but rather means to put probabilistic bounds on the relative frequency or likelihood of occurrence of future uncertain

3. Are we able to develop a rigorous, mathematical argument regarding randomness? Before we begin to answer these questions, we will present definitions from the literature to facilitate the discussion. 1 1 Definitions Two ubiquitous concept used in studies of randomness are ”the gambler’s fal lacy” and ”the hot hand.”

We live in a scientific world were the results of published research findings can dictate our very existence. Yet, there is an increasing body of evidence that suggest that “most publish research findings are false” (Ioannidis, 2005 page 0696). How can this be true? Part1: According to Ioannidis (2005), “the pre-study probability of a relationship being true is R/ (R + 1). Where R is the ratio of the number of true relationships to no relationships among those tested in the field” (page 0696). The Null Hypothesis (Ho) is what you want to disprove, what you want to prove to be not true. The Alternative hypothesis (HA) on the other hand is what you want to prove to be true. Thus, in scientific research we are looking to prove that relationships are true or to prove that they are not true. The power of a statistical test is defined as the ability of the test to lead to a conclusion to accept the HA when in fact, the HA is true (Wirtz, 2013). Also, since the probability of a statistical study depends on the prior probability, statistical power, and the level of the observed P value, it means that the probability of a study finding a true relationship is the power of 1-β (one – type two error (Ioannidis, 2005 page 0696). Also, “type 1 error is the probability of incorrectly rejecting a null hypothesis that should not be rejected” (Wirtz, 2013). Factors that negatively affect the probability of true relationships are small studies, smaller effect sizes, in a scientific field,

Cauchy’s was the first mathematician to consider probability theory as “pure” mathematics. He found an upper bond to the difference between the exact value and the approximation and then specified conditions for those bound to tend to zero. The problem with his theorem was that it was not proven for distributions with

Bernoulli numbers evaluate the probability of a sequence of rational numbers. They’re found commonly within many types of mathematics: Number Theory, Euler-Maclaurin summation, and power series are some exampled. Once Bernoulli’s ideas were published, it gave flight to many mathematicians in the field of probability. You can consider Jakob Bernoulli as the founding father of probability.

Economics is partially mathematical science and partially a study in human psychology. Both financial and psychological factors affect the behavior of investors and the marketplace. For example, one popular theory known as expectations theory is based upon the "hypothesis that long-term interest rates contain a prediction of future short-term interest rates. Expectations theory postulates that you would earn the same amount of interest by investing in a one-year bond today and rolling that investment into a new one-year bond a year later compared to buying a two-year bond today" (Expectations theory, 2012, Investopedia). In other words, a certain consistency is assumed regarding rates, even though many analysts have noted that this simple and elegant theory is often inaccurate and tends to overstate gains (Expectations theory, 2012, Investopedia).