The popular Monty Hall Problem is about being on a game show where you’re either going to win a fancy sports car or a goat. It’s a no brainer on which one you would prefer: the car. You have to choose between three doors. Behind two of the doors are goats and the fancy car is the last one. Whichever door you choose, the prize behind it is yours. The sample space is one thing to consider in this problem. There is a winning door and the two remaining doors are x and y and have goats behind them. If the contestant chooses door x or door y, which has the car behind it, the sample space would have nine outcomes: S ={(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}. Being the contestant, you would think that it doesn’t…
This uncertainty includes the quantities resulting from lack of sufficient information. Another important concept in Bayesian methods are the need to determine the prior probability distribution (probability distribution describing our beliefs about the uncertainty in the model before data becomes available) taking into account the available information. Generally, Bayesian methods involve the sequential application of the Bayes formula and the steps in these methods can be summarized as…
"Struck by Lightning: the curious world of probabilities" is a book written in 2005 by Jeffrey S. Rosenthal, an award-winning Canadian statistician and author. Jeffrey S. Rosenthal graduated from Woburn Collegiate Institute in 1984, received his B.Sc. in mathematics, physics and computer science in Toronto in 1988. He later received his PhD in mathematics in Harvard University in 1992. He performs music and improv. comedy as well as being an author and supervisor of student projects. "Struck by…
Probability concepts like faith, as it exists in the dim intuition, through school education, the surface of that understanding, intuition often conflicts that again with a different point of view, must be thinking more in-depth study to be able to understand. Hot Monty Hall problem, and that is one example. There is not a simple probability, long confused with so many people and academics, the more deeply ponder the problems found. Since 1990, 1991 flared up in hot to 2000, there are more…
as numeracy. Age. Older individuals don’t understand risk information as well, both overestimate and underestimate probabilities (Fuller, Dudley, & Blacktop, 2001), worse risk comprehension than younger individuals (Fausset & Rogers, 2012). Much of the literature supports the idea that decision making effectiveness…
The VCE mathematics topic that I have chosen is Probability, in Mathematical Methods Unit 1 Area Study 4: Probability and Statistics (VCAA, 2015). The first section presents a literature review of student learning probability. It also addresses the common pitfalls that may impede their learning. The second section outlines a unit plan for teaching probability based on the new VCE study design. Sample activities worksheets and assessment tasks are included in the appendices. Literature Review:…
There is no inventor, known contributors, and early uses. For instance, one can find the true and false values for a computer program. P(A|B) = P (A (B) / P (B) is the conditional probability representation. In additional, truth tables and probability are today uses. Bayes Theorem is the final concept in statistics, which is defined as the description of the probability of events based on related conditions. Thomas Bayes developed P (A|B) = P (B|A) (P (A) / P (B) where Pierre-Simon Laplace…
uncertainty. When an “outcome is the result of adding the outcomes of many separate performances, all in certain respects uniform”; in other words, when the frequency-ratio is known, then the experiment is named divisible, while a non-divisible or non-seriable experiment is one which “can be neither itself broken down into a number of uniform additive parts nor treated as part of a divisible experiment” (p. 8). In a non-divisible experiment the frequency-ratio standpoint has no actual sense. One…
2005). In Li (2000) paper, a new random variable named ‘time-until-default’ was created to demonstrate survival time of each defaultable entity. And the copula function approach is based on this random variable to evaluate the default probability of financial instruments. Specifically, copula function specify the joint distribution of the survival times after using the market information to derive the marginal distribution of the survival time. This approach solves the default correlation and…
In definition, probability refers to the measure of the likelihood of an event happening. The probability for any event occurring falls between 1 percent and 100 percent thus meaning that the interpreted meaning of a probability equals the subject meaning held of the probability (Grinstead et al, 1997). However, it is worth noting that the application of probability or assigning of probability to the events in the effort to gratifying the axioms of probability follows some rules or basics…