...Americans for decades have been sheepishly led into believing most all historical events are heroic and morally correct. Students today need to learn about every possible aspect of any given subject. Though most would prefer not to be taught or lectured on the darker side of certain historic events, it is becoming more and more necessary. One of the most popular events in history is when chistopher columbus "discovered america". It has been precieved as a happy go-lucky time through the years by disney movies, with love stories and happy endings to school plays, and holiday such as columbus day and thanksgiving. Though most resources are very informative they can also be quite misleading. Columbus and his voyages consisted of betrayal, slavery,...
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...Factors Affecting the Study Habits of Criminology Students of Basc Teaching Grammar What is grammar? ’An abstract system of rules whereby a person’s mastery of their native language can be explained’ (dictionary definition) Different dictionaries define ’grammar’ in different ways, but they all effectively talk about the ’rules of the language’. Grammar does not equal only ’tenses’ or verb forms. Grammar is language and how we use it. What is more important than a definition of the word ’grammar’ is knowing what students need to know when they are learning grammar. And we also need to know different ways to teach grammar. There are many different methods to teach grammar, but the three that might be the most effective in retaining student interest are the following: 1. Situational Presentations 2. Text and Recordings 3. Test Teach Test 1. Teaching grammar via Situational Presentation I. What do students need to know? When presenting new language, the teacher must show following things very clearly: MPF: There are several aspects of a new item: that you need to know and learners need to learn. 1. What it means. They need to understand meaning within the given context. 2. What it sounds like. They need to know the natural pronunciation and spelling of the language. 3. What it looks like. They need to know how to form the language (how it is constructed). 4. How and when it is used. They need to know the function of the language...
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...AS History Unit Two – 6522E Italy; The rise of Fascism: 1918- 1925 Summary The main focus of this topic is how the changing political situation in Italy after the First World War led to the rise of Fascism in the years to 1922 and the ways in which the Fascist Party established itself in power in Italy in the years 1922-1925: ▪ Weaknesses of the Liberal state, 1918-1922 ▪ Mussolini, the message and appeal of Fascism, its changing focus from 1919-1922 ▪ Support for, and opposition to, Fascism among different social groups ▪ The consolidation of Fascist power, 1922-1925 Examination You will be required to tackle one two-part structured question from a choice of two. The first sub-question (a) will be worth 20 marks, whilst the second sub-question (b) will be worth 40 marks. The total mark for this exam is 60. The examination will last for 55 minutes and can be taken in either January or June. There is a difference between question (a), which is a ‘describe’ question, and (b) which is an ‘explain’ question. This can be briefly outlined as follows: ‘Describe’ These will ask you to select information from your memory and describe what happened. They may ask you to describe a series of events, the way in which something, or someone was important, or the way in which something changed over time. Your answer should contain: 1) A very short introduction with an outline of your overall argument. 2) A series of different...
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...“Every artist dips his brush in his own soul, and paints his own nature into his pictures” - Henry Ward Beecher “I experience a period of frightening clarity in those moments when nature is so beautiful. I am no longer sure of myself, and the painting appears as in a dream” - Vincent van Gogh It is wide-spread knowledge that all ingenious people are a little strange, that their minds work in ways completely different to ours, that their perspective of reality is unlike that of common people. Take Picasso for instance: his vision of reality was utterly different than what you or I see. What about Salvador Dali and his eccentric work? No need to go that far, Vincent Van Gogh himself was a peculiar person. Those are people who likely experienced the above mentioned frightening clarity. When those people sat down to paint, they put a piece of their soul into the canvas; otherwise their work would never have been even half as good! Let’s simplify: if this class sits down and we are given the same assignment: draw a landscape, every single image will be different. Every single person will put a piece of their personality on paper. For those who were not born with that eccentricity, there was always the little chemical helper: Sigmund Freud used cocaine to help write papers, P.I. Tchaikovsky was friendly with the bottle and the fictional Sherlock Holmes induced himself with cocaine or heroin to get his brain working. People inducing themselves with drugs is not that new as...
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...Permutations The word ‘coincidence’ is defined as an event that might have been arranged though it was accidental in actuality. Most of us perceive life as a set of coincidences that lead us to pre-destined conclusions despite believing in a being who is free from the shackles of time and space. The question is that a being, for whom time and space would be nothing more than two more dimensions, wouldn’t it be rather disparaging to throw events out randomly and witness how the history unfolds (as a mere spectator)? Did He really arrange the events such that there is nothing accidental about their occurrence? Or are all the lives of all the living beings merely a result of a set of events that unfolded one after another without there being a chronological order? To arrive at satisfactory answers to above questions we must steer this discourse towards the concept of conditional probability. That is the chance of something to happen given that an event has already happened. Though, the prior event need not to be related to the succeeding one but must be essential for it occurrence. Our minds as I believe are evolved enough to analyze a story and identify the point in time where the story has originated or the set of events that must have happened to ensure the specific conclusion of the story. To simplify the conundrum let us assume a hypothetical scenario where a man just became a pioneer in the field of actuarial science. Imagine him telling us his story in reverse. “I became...
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...the stage where one can begin to use probabilistic ideas in statistical inference and modelling, and the study of stochastic processes. Probability axioms. Conditional probability and independence. Discrete random variables and their distributions. Continuous distributions. Joint distributions. Independence. Expectations. Mean, variance, covariance, correlation. Limiting distributions. The syllabus is as follows: 1. Basic notions of probability. Sample spaces, events, relative frequency, probability axioms. 2. Finite sample spaces. Methods of enumeration. Combinatorial probability. 3. Conditional probability. Theorem of total probability. Bayes theorem. 4. Independence of two events. Mutual independence of n events. Sampling with and without replacement. 5. Random variables. Univariate distributions - discrete, continuous, mixed. Standard distributions - hypergeometric, binomial, geometric, Poisson, uniform, normal, exponential. Probability mass function, density function, distribution function. Probabilities of events in terms of random variables. 6. Transformations of a single random variable. Mean, variance, median, quantiles. 7. Joint distribution of two random variables. Marginal and conditional distributions. Independence. iii iv 8. Covariance, correlation. Means and variances of linear functions of random variables. 9. Limiting distributions in the Binomial case. These course notes explain the naterial in the syllabus. They have been “fieldtested” on the class of 2000...
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...by the emergence of the core values of Western-type society: the relations of private ownership, private production, market-oriented, the first “government by the people” – democracy, republican form of government. In the early times of Western Civilization the foundations of civil society to ensure individual rights and freedoms were established, as well as socio-cultural system of principles, the mobilization of creativity and development of the individuals (Judith & Learner, 130). There are many significant events that happened in Western Civilization and influenced today`s world, as some of them have significantly affected our modern lifestyle and undoubtedly changed our society. Nevertheless, I think the three major elements that happened in Western Civilization are: The Rise of Christianity, the appearance of Democracy, and the invention of the printing press. To start with, I strongly believe the Rise of Christianity is one of the most significant events that have ever happened in our world. In today`s world Christianity is thought to be the biggest religion, as about 2, 1 billion people follow it. This religion is based on teachings of Jesus Christ, who is believed to be the Son of God (Engels, 46). Based on Jesus preaching and...
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...THE MATHEMATICS OF LOTTERY Odds, Combinations, Systems ∏ Cătălin Bărboianu INFAROM Publishing Applied Mathematics office@infarom.com http://www.infarom.com http://probability.infarom.ro ISBN 978-973-1991-11-5 Publisher: INFAROM Author: Cătălin Bărboianu Correction Editor: CarolAnn Johnson Copyright © INFAROM 2009 This work is subject to copyright. All rights are reserved, whether the whole work or part of the material is concerned, specifically the rights of translation, reprinting, reuse of formulas and tables, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of Copyright Laws, and permission for use must always be obtained from INFAROM. 2 Contents (of the complete edition) Introduction ...................................................................................... 5 The Rules of Lottery ...................................................................…. 11 Supporting Mathematics ......................................................…....... 15 Probability space ..............................................................…......... 16 Probability properties and formulas used .........................…......... 19 Combinatorics …………………………………………………... 22 Parameters of the lottery matrices …………………………......... 25 Number Combinations .......………….………………………...
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...Unit 2 DB Subjective Probability “ A probability derived from an individual's personal judgment about whether a specific outcome is likely to occur. Subjective probabilities contain no formal calculations and only reflect the subject's opinions and past experience.” (investopedia.com, 2013) There are three elements of a probability which combine to equal a result. There is the experiment ,the sample space and the event (Editorial board, 2012). In this case the class is the experiment because the process of attempting it will result in a grade which could vary from an A to F. The different grades that can be achieved in the class are the sample space. The event or outcome is the grade that will be received at the end of the experiment. I would like to achieve an “A” in this class but due to my lack of experience in statistical analysis, my hesitation towards advanced mathematics, and the length of time it takes for me to complete my course work a C in this class may be my best result. I have a 1/9 chance or probability to receive an “A” in the data range presented to me which is (A,A-,B,B-,C,C-,D,D- AND F). By the grades that have been posted I would say that the other students have a much better chance of receiving a better grade than mine. I have personally use subjective probability in my security guard business in bidding on contracts based on the clients involved , the rates that I charge versus the rates other companies charge and the amount of work involved...
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... Probability – the chance that an uncertain event will occur (always between 0 and 1) Impossible Event – an event that has no chance of occurring (probability = 0) Certain Event – an event that is sure to occur (probability = 1) Assessing Probability probability of occurrence= probability of occurrence based on a combination of an individual’s past experience, personal opinion, and analysis of a particular situation Events Simple event An event described by a single characteristic Joint event An event described by two or more characteristics Complement of an event A , All events that are not part of event A The Sample Space is the collection of all possible events Simple Probability refers to the probability of a simple event. Joint Probability refers to the probability of an occurrence of two or more events. ex. P(Jan. and Wed.) Mutually exclusive events is the Events that cannot occur simultaneously Example: Randomly choosing a day from 2010 A = day in January; B = day in February Events A and B are mutually exclusive Collectively exhaustive events One of the events must occur the set of events covers the entire sample space Computing Joint and Marginal Probabilities The probability of a joint event, A and B: Computing a marginal (or simple) probability: Probability is the numerical measure of the likelihood that an event will occur The probability of any event must be between 0 and 1, inclusively The sum of the...
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...= {-20, -19, …, -1, 0, 1, …, 19, 20} Number of people arriving at a bank in a day: S = {0, 1, 2, …} Inspection of parts till one defective part is found: S = {d, gd, ggd, gggd, …} Temperature of a place with a knowledge that it ranges between 10 degrees and 50 degrees: S = {any value between 10 to 50} Speed of a train at a given time, with no other additional information: S = {any value between 0 to infinity} 4 Sample Space (cont…) Discrete sample space: One that contains either finite or countable infinite set of outcomes • Out of the previous examples, which ones are discrete sample spaces??? Continuous sample space: One that contains an interval of real numbers. The interval can be either finite or infinite 5 Events A collection of certain sample points A subset of the sample space Denoted by ‘E’ Examples: • Getting an odd number in dice throwing experiment S = {1, 2, 3, 4,...
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...[pic] [pic] Markov Chain [pic] Bonus Malus Model [pic] [pic] This table justifies the matrix above: | | | |Next state | | | |State |Premium |0 Claims |1 Claim |2 Claims |[pic]Claims | |1 | |1 |2 |3 |4 | |2 | |1 |3 |4 |4 | |3 | |2 |4 |4 |4 | |4 | |3 |4 |4 |4 | | | | | | | | |P11 |P12 |P13 |P14 | | | |P21 |P22 |P23 |P24 | | | |P31 |P32 |P33 |P34 | | | |P41 |P42 |P43 |P44 | | | | ...
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...presence with probability 0.99. If it is not present, the radar falsely registers an aircraft presence with probability 0.10. We assume that an aircraft is present with probability 0.05. What is the probability of false alarm (a false indication of aircraft presence), and the probability of missed detection (nothing registers, even though an aircraft is present)? A sequential representation of the sample space is appropriate here, as shown in Fig. 1. Figure 1: Sequential description of the sample space for the radar detection problem Solution: Let A and B be the events A={an aircraft is present}, B={the radar registers an aircraft presence}, and consider also their complements Ac={an aircraft is not present}, Bc={the radar does not register an aircraft presence}. The given probabilities are recorded along the corresponding branches of the tree describing the sample space, as shown in Fig. 1. Each event of interest corresponds to a leaf of the tree and its probability is equal to the product of the probabilities associated with the branches in a path from the root to the corresponding leaf. The desired probabilities of false alarm and missed detection are P(false alarm)=P(Ac∩B)=P(Ac)P(B|Ac)=0.95∙0.10=0.095, P(missed detection)=P(A∩Bc)=P(A)P(Bc|A)=0.05∙0.01=0.0005. Application of Bayes` rule in this problem. We are given that P(A)=0.05, P(B|A)=0.99, P(B|Ac)=0.1. Applying Bayes’ rule, with A1=A and A2=Ac, we obtain P(aircraft present | radar registers) =...
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...1.M/G/ Queue a. Show that Let A(t) : Number of arrivals between time (0, t] “ n should be equal to or great than k” since if n is less than k (n<k), Pk(t)=0 Let’s think some customer C, Let’s find P{C arrived at time x and in service at time t | x=(0,t)] } P{C arrives in (x, x+dx] | C arrives in (0, t] }P{C is in service | C arrives at x, and x = (0,t] } Since theorem of Poisson Process, The theorem is that Given that N(t) =n, the n arrival times S1, S2, …Sn have the same distribution as the order statistics corresponding to n independent random variables uniformly distributed on the interval (0, t) Thus, P{C is in service | C arrives between time (0, t] } Since let y=t-x, x=0 → y=t, x=t →y=o, dy=-dx Therefore, In conclusion, ------ (1) 1-a Solution Since b. let 1-b Solution ------------------------------------------------- 2. notation Page 147 in “Fundamentals of Queuing Theory –Third Edition- , Donald Gross Carl M. Harris a. b. ------------------------------------------------- ------------------------------------------------- ------------------------------------------------- 3. a. let X=service time (Random variable) and XT=total service time (Random variable) X2=X+X, X3=X+X+X, ….. f2(x2)...
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...Probability & Mathematical Statistics | “The frequency concept of Probability” | [Type the author name] | What is probability & Mathematical Statistics? It is the mathematical machinery necessary to answer questions about uncertain events. Where scientists, engineers and so forth need to make results and findings to these uncertain events precise... Random experiment “A random experiment is an experiment, trial, or observation that can be repeated numerous times under the same conditions... It must in no way be affected by any previous outcome and cannot be predicted with certainty.” i.e. it is uncertain (we don’t know ahead of time what the answer will be) and repeatable (ideally).The sample space is the set containing all possible outcomes from a random experiment. Often called S. (In set theory this is usually called U, but it’s the same thing) Discrete probability Finite Probability This is where there are only finitely many possible outcomes. Moreover, many of these outcomes will mostly be where all the outcomes are equally likely, that is, uniform finite probability. An example of such a thing is where a fair cubical die is tossed. It will come up with one of the six outcomes 1, 2, 3, 4, 5, or 6, and each with the same probability. Another example is where a fair coin is flipped. It will come up with one of the two outcomes H or T. Terminology and notation. We’ll call the tossing of a die a trial or an experiment. Where we...
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