Ruin Probabilities - UNL Math - University of Nebraska–Lincoln
... Why do we hear about people who actually win? We often hear from people who consistently win at the casino. How can this be in the face of the theorems above? A simple illustration makes clear how this is possible. Assume for convenience a gambler who repeatedly visits the casino, each time with a c ...
... Why do we hear about people who actually win? We often hear from people who consistently win at the casino. How can this be in the face of the theorems above? A simple illustration makes clear how this is possible. Assume for convenience a gambler who repeatedly visits the casino, each time with a c ...
What Could Be Objective About Probabilities
... state changes with time. In a deterministic system, specification of the state of the system at one time together with the dynamics determines the state at later times. 1 In an indeterministic system, the state of a system at one time and the laws are jointly compatible with different states at late ...
... state changes with time. In a deterministic system, specification of the state of the system at one time together with the dynamics determines the state at later times. 1 In an indeterministic system, the state of a system at one time and the laws are jointly compatible with different states at late ...
What Could Be Objective About Probabilities
... state changes with time. In a deterministic system, specification of the state of the system at one time together with the dynamics determines the state at later times. 1 In an indeterministic system, the state of a system at one time and the laws are jointly compatible with different states at late ...
... state changes with time. In a deterministic system, specification of the state of the system at one time together with the dynamics determines the state at later times. 1 In an indeterministic system, the state of a system at one time and the laws are jointly compatible with different states at late ...
Declarations of Independence
... In his classic textbook, Billingsley (1995) writes that “the conditional probability of a set A with respect to another set B … is defined of course by P(A|B) = P(A ∩ B)/P(B), unless P(B) vanishes, in which case it is not defined at all” (427). Three things leap out at us here: the ratio is regarded ...
... In his classic textbook, Billingsley (1995) writes that “the conditional probability of a set A with respect to another set B … is defined of course by P(A|B) = P(A ∩ B)/P(B), unless P(B) vanishes, in which case it is not defined at all” (427). Three things leap out at us here: the ratio is regarded ...
The Justification of Probability Measures in Statistical Mechanics*
... that an isolated system in a medium-entropy state is much more likely to have had a high-entropy past than a low-entropy past, contrary to our experience. Some sort of maneuvering is therefore needed in order to salvage our ability to reason about the past using statistical mechanics. Precisely what ...
... that an isolated system in a medium-entropy state is much more likely to have had a high-entropy past than a low-entropy past, contrary to our experience. Some sort of maneuvering is therefore needed in order to salvage our ability to reason about the past using statistical mechanics. Precisely what ...
Probability and Information Theory
... discrete cell that it was observed to occupy. In many cases, it is more practical to use a simple but uncertain rule rather than a complex but certain one, even if the true rule is deterministic and our modeling system has the fidelity to accommodate a complex rule. For example, the simple rule “Most ...
... discrete cell that it was observed to occupy. In many cases, it is more practical to use a simple but uncertain rule rather than a complex but certain one, even if the true rule is deterministic and our modeling system has the fidelity to accommodate a complex rule. For example, the simple rule “Most ...
john maynard keynes and ludwig von mises on probability
... be maintained. If the samples relate to historical periods far enough from each other to render the assumption of independence plausible, one is unlikely to get homogeneous samples; thus invalidating the ‘experiment’. In the second case the use of a sample of cross-section data would still not give ...
... be maintained. If the samples relate to historical periods far enough from each other to render the assumption of independence plausible, one is unlikely to get homogeneous samples; thus invalidating the ‘experiment’. In the second case the use of a sample of cross-section data would still not give ...
From Cournot`s Principle to Market Efficiency
... in advance will not happen. From the turn of the twentieth century through the 1950s, many mathematicians, including Chuprov, Borel, Fréchet, Lévy, and Kolmogorov, saw this principle as fundamental to the application and meaning of probability.1 In their view, a probability model gains empirical c ...
... in advance will not happen. From the turn of the twentieth century through the 1950s, many mathematicians, including Chuprov, Borel, Fréchet, Lévy, and Kolmogorov, saw this principle as fundamental to the application and meaning of probability.1 In their view, a probability model gains empirical c ...
The "slippery" concept of probability: Reflections on possible
... The Relationship Between Probability and Data Handling: The Malati approach to the study of probability and data handling was based on the developers’ conceptual understanding of the two topics. Probability was presented before data handling as it was felt that an understanding of the concepts of ch ...
... The Relationship Between Probability and Data Handling: The Malati approach to the study of probability and data handling was based on the developers’ conceptual understanding of the two topics. Probability was presented before data handling as it was felt that an understanding of the concepts of ch ...
Transcription
... the first marble isn’t replaced. Also, we must decrease the numerator by one if it is a compound event where we are choosing the same color twice. Without completing any calculations, what will be the probability of choosing two blues in a row? The probability will be zero. Explain how you know this ...
... the first marble isn’t replaced. Also, we must decrease the numerator by one if it is a compound event where we are choosing the same color twice. Without completing any calculations, what will be the probability of choosing two blues in a row? The probability will be zero. Explain how you know this ...
Objective probability and the assessment of
... physical property of a coin that it lands heads as often as tails. The suggestive terms ‘would be’ and ‘habit’ were used by C. S. Peirce to describe such characteristics.21 Things are a little more complex than these examples suggest, however. A coin thrown onto a slotted board can land on its side ...
... physical property of a coin that it lands heads as often as tails. The suggestive terms ‘would be’ and ‘habit’ were used by C. S. Peirce to describe such characteristics.21 Things are a little more complex than these examples suggest, however. A coin thrown onto a slotted board can land on its side ...
The Bayesian Controversy in Statistical Inference
... speeds bring out different aspects of the work, and has on this occasion really made an arbitrary choice. Or again, in a more important context, if we were to insist that, in any given state of knowledge, there was always a ‘best’ indicated method of treatment of a diseased patient, we would pose ex ...
... speeds bring out different aspects of the work, and has on this occasion really made an arbitrary choice. Or again, in a more important context, if we were to insist that, in any given state of knowledge, there was always a ‘best’ indicated method of treatment of a diseased patient, we would pose ex ...
John Tabak-Probability and Statistics_ The Science of Uncertainty
... One of the earliest devices for producing random patterns for which there is direct evidence is the astragalus, a bone found in the heels of deer, sheep, dogs, and other mammals. When thrown, the astragalus can land on any of four easy-to-distinguish sides. Many astragali have been found at prehisto ...
... One of the earliest devices for producing random patterns for which there is direct evidence is the astragalus, a bone found in the heels of deer, sheep, dogs, and other mammals. When thrown, the astragalus can land on any of four easy-to-distinguish sides. Many astragali have been found at prehisto ...
Conditional Probability
... NOT graduate. In symbols, you can conclude P(GC|W)=0.40. In both conditional probabilities, you are conditioning on the same group of people, students with off-campus jobs. If 60% of those students graduate, the other 40% of those students do not. Unfortunately, many people make the mistake of doing ...
... NOT graduate. In symbols, you can conclude P(GC|W)=0.40. In both conditional probabilities, you are conditioning on the same group of people, students with off-campus jobs. If 60% of those students graduate, the other 40% of those students do not. Unfortunately, many people make the mistake of doing ...
Document
... Probability with Combinations Ex. 1 12 male and 16 female students have been selected as equal qualifiers for 6 college scholarships. If the qualifiers interviewed on the first day are to be chosen at random, what is the probability that 3 will be male and 3 female? 1. Determine the number of succe ...
... Probability with Combinations Ex. 1 12 male and 16 female students have been selected as equal qualifiers for 6 college scholarships. If the qualifiers interviewed on the first day are to be chosen at random, what is the probability that 3 will be male and 3 female? 1. Determine the number of succe ...
Philosophies of Probability
... in 2010, and thus there is a natural propensity interpretation. Suppose, on the other hand, that V contains single-case variables A and B, standing for age of car with registration AB01 CDE on January 1st 2010 and breakdown in last year of car with registration AB01 CDE on January 1st 2010. Then V d ...
... in 2010, and thus there is a natural propensity interpretation. Suppose, on the other hand, that V contains single-case variables A and B, standing for age of car with registration AB01 CDE on January 1st 2010 and breakdown in last year of car with registration AB01 CDE on January 1st 2010. Then V d ...
Relative frequencies
... is, A (1)-or-A (2)-or-A (3)-or ... ; symbolically u{A (n) : n EN} - has relative frequency 1. It is an event that happens every day. So relative frequency is not countably additive. 2 Indeed, its domain of definition is not closed under countable unions, and so is not a Borel field. For let B be an ...
... is, A (1)-or-A (2)-or-A (3)-or ... ; symbolically u{A (n) : n EN} - has relative frequency 1. It is an event that happens every day. So relative frequency is not countably additive. 2 Indeed, its domain of definition is not closed under countable unions, and so is not a Borel field. For let B be an ...
The Axioms of Subjective Probability
... and Probability,to the present. My hope is that this will not only provide a useful currentperspectiveon subjectiveprobabilityper se but that it will also promote appreciation of a vital part of the Bayesian approach to statistical decision theorypioneered by Good (1950) and Savage (1954) and furthe ...
... and Probability,to the present. My hope is that this will not only provide a useful currentperspectiveon subjectiveprobabilityper se but that it will also promote appreciation of a vital part of the Bayesian approach to statistical decision theorypioneered by Good (1950) and Savage (1954) and furthe ...
The expansion of random regular graphs
... We will work only with labelled n-vertex graphs; from now on, ‘a graph on [n]’ will always mean a labelled graph on [n]. Recall that if A1 , A2 , . . . is a sequence of events in probability spaces Ω1 , Ω2 , . . ., we say that ‘An occurs with high probability’ if P(An ) → 1 as n → ∞. In this languag ...
... We will work only with labelled n-vertex graphs; from now on, ‘a graph on [n]’ will always mean a labelled graph on [n]. Recall that if A1 , A2 , . . . is a sequence of events in probability spaces Ω1 , Ω2 , . . ., we say that ‘An occurs with high probability’ if P(An ) → 1 as n → ∞. In this languag ...
Slides - Rutgers Statistics
... that when I am making a choice, I must regard it as free. In doing so, I cannot assign probabilities to my acting in one way rather than another (even though onlookers may be able to do so). ...
... that when I am making a choice, I must regard it as free. In doing so, I cannot assign probabilities to my acting in one way rather than another (even though onlookers may be able to do so). ...
Bayesianism with a Human Face - Minnesota Center for Philosophy
... probability theory proper. Whereas Bayes's rule in Glymour's sense prescribes conditioning as the way to update personal probabilities, Bayes's rule in my sense prescribes what Wald (1950) called "Bayes solutions" to decision problems, i.e., solutions that maximize expected utility relative to some ...
... probability theory proper. Whereas Bayes's rule in Glymour's sense prescribes conditioning as the way to update personal probabilities, Bayes's rule in my sense prescribes what Wald (1950) called "Bayes solutions" to decision problems, i.e., solutions that maximize expected utility relative to some ...
Tutorial: Defining Probability for Science.
... Defining probability as a ratio of events is often referred to as the frequentist definition and is the one with which scientists will be most familiar. For an example, if an experiment is performed N times and a certain outcome Ei occurs in M of these cases then as N → ∞ we can say M/N → P (Ei ). T ...
... Defining probability as a ratio of events is often referred to as the frequentist definition and is the one with which scientists will be most familiar. For an example, if an experiment is performed N times and a certain outcome Ei occurs in M of these cases then as N → ∞ we can say M/N → P (Ei ). T ...
The Principle of Sufficient Reason and Probability
... “chance” to indicate probabilities that are the tendencies of stochastic processes. Consider now this simple inference. A coin has been independently flipped a thousand times, and about 750 times the coin has landed heads. There is a very natural inference: The coin is loaded in such a way as to hav ...
... “chance” to indicate probabilities that are the tendencies of stochastic processes. Consider now this simple inference. A coin has been independently flipped a thousand times, and about 750 times the coin has landed heads. There is a very natural inference: The coin is loaded in such a way as to hav ...
Probability of One Event
... Matthew decides to try to estimate the probability that toast lands butter-sidedown when dropped. He drops a piece of buttered toast 50 times and observes that it lands butter-side-down 30 times. Estimate the probability that the toast lands butter-side-down. ...
... Matthew decides to try to estimate the probability that toast lands butter-sidedown when dropped. He drops a piece of buttered toast 50 times and observes that it lands butter-side-down 30 times. Estimate the probability that the toast lands butter-side-down. ...
How bad is a 10% chance of losing a toe?
... scales represented expected disutility. Thus, although we should expect both of these scales to be monotonically related to EU, we should not expect them to be linearly related. Each response scale could be some transform of EU. Thus, we transformed the variables for each subject so that the transfo ...
... scales represented expected disutility. Thus, although we should expect both of these scales to be monotonically related to EU, we should not expect them to be linearly related. Each response scale could be some transform of EU. Thus, we transformed the variables for each subject so that the transfo ...
History of randomness
In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. At the same time, most ancient cultures used various methods of divination to attempt to circumvent randomness and fate.The Chinese were perhaps the earliest people to formalize odds and chance 3,000 years ago. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the sixteenth century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of modern calculus had a positive impact on the formal study of randomness. In the 19th century the concept of entropy was introduced in physics.The early part of the twentieth century saw a rapid growth in the formal analysis of randomness, and mathematical foundations for probability were introduced, leading to its axiomatization in 1933. At the same time, the advent of quantum mechanics changed the scientific perspective on determinacy. In the mid to late 20th-century, ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness.Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the twentieth century computer scientists began to realize that the deliberate introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases, such randomized algorithms are able to outperform the best deterministic methods.