Learning Objectives Definition Experiment, Outcome, Event
... • There is a diagnostic technique to detect the disease, but it is not very accurate. Let B denote the event “test shows the disease is present.” Assume that historical evidence shows that if a person actually has the disease, the probability that the test will indicate the presence of the disease i ...
... • There is a diagnostic technique to detect the disease, but it is not very accurate. Let B denote the event “test shows the disease is present.” Assume that historical evidence shows that if a person actually has the disease, the probability that the test will indicate the presence of the disease i ...
Powerpoint
... • trial 1: pick a ball – event E1 = the ball is red • do not replace the ball in the bag • trial 2: pick a ball – event E2 = the ball is red What is the probability of the event E, where E = picking two red balls on successive trials (without replacement)? In this case, the probability of E2 is affe ...
... • trial 1: pick a ball – event E1 = the ball is red • do not replace the ball in the bag • trial 2: pick a ball – event E2 = the ball is red What is the probability of the event E, where E = picking two red balls on successive trials (without replacement)? In this case, the probability of E2 is affe ...
Bayesian, Likelihood, and Frequentist Approaches to Statistics
... urn-sampling problem that we had drawn a white ball. The probability of sampling a white ball is 3/4 if A is chosen and 1/2 if B is chosen. These are the so-called likeliAugust 2003 ...
... urn-sampling problem that we had drawn a white ball. The probability of sampling a white ball is 3/4 if A is chosen and 1/2 if B is chosen. These are the so-called likeliAugust 2003 ...
Interpreting Probability - Assets - Cambridge
... assess voting procedures. Probabilists such as Laplace, however, tended not to notice that inverting the equations changed the meaning of probability. The probability of picking a ball of a particular color was a function of the relative proportions in the urn. The probability of guilt was different ...
... assess voting procedures. Probabilists such as Laplace, however, tended not to notice that inverting the equations changed the meaning of probability. The probability of picking a ball of a particular color was a function of the relative proportions in the urn. The probability of guilt was different ...
Lecture 5: Hashing with real numbers and their big-data applications
... number of possible IP addresses is 2128 , which is too large to let us have a table indexed by IP addresses. Hashing allows us to rename each IP address by fewer bits. In Lecture 1 this hash was a number in a finite field (integers modulo a prime p). In recent years large data algorithms have used h ...
... number of possible IP addresses is 2128 , which is too large to let us have a table indexed by IP addresses. Hashing allows us to rename each IP address by fewer bits. In Lecture 1 this hash was a number in a finite field (integers modulo a prime p). In recent years large data algorithms have used h ...
and “Random” to Meager, Shy, etc.
... Instead of properties, it is reasonable to talk about sets. Every property P (x) defines a set, namely, the set {x : P (x)} of all the objects that satisfy this property. However, not all sets correspond to what we intuitively mean by properties. Indeed, in statistics, properties must be well defined ...
... Instead of properties, it is reasonable to talk about sets. Every property P (x) defines a set, namely, the set {x : P (x)} of all the objects that satisfy this property. However, not all sets correspond to what we intuitively mean by properties. Indeed, in statistics, properties must be well defined ...
Derivation of Binomial Probability Formula
... observed rather than being given explicit knowledge of the makeup of the group and then examining a subset of it. For this reason, we must employ different techniques from those used in other cases. For simplicity’s sake, rather than work with a total of 24 peas, let us consider the simpler case of ...
... observed rather than being given explicit knowledge of the makeup of the group and then examining a subset of it. For this reason, we must employ different techniques from those used in other cases. For simplicity’s sake, rather than work with a total of 24 peas, let us consider the simpler case of ...
The Optimality of Correlated Sampling
... Alice and Bob are given distributions P and Q respectively over the same universe Ω. Without any interaction, Alice is required to output an element i ∼ P and Bob is required to output an element j ∼ Q, where the players have access to shared randomness. The goal is to minimize the disagreement prob ...
... Alice and Bob are given distributions P and Q respectively over the same universe Ω. Without any interaction, Alice is required to output an element i ∼ P and Bob is required to output an element j ∼ Q, where the players have access to shared randomness. The goal is to minimize the disagreement prob ...
8.6 Practice set 3 - School District 27J
... You flip a coin 7 times in a row. Use a simulation to determine the probability distribution for the number of times the coin lands heads up. A When you flip a coin, the possible outcomes are heads and tails. You will use your ...
... You flip a coin 7 times in a row. Use a simulation to determine the probability distribution for the number of times the coin lands heads up. A When you flip a coin, the possible outcomes are heads and tails. You will use your ...
Why Simple Hash Functions Work: Exploiting the Entropy in a Data
... at least m+2 log(T /ε) and H is a random universal hash function mapping to {0, 1}m , then (H(X1 ), . . . , H(XT )) has statistical difference at most ε from T uniform and independent elements of {0, 1}m . Thus, any event that would occur with some probability p under ideal hashing now occurs with p ...
... at least m+2 log(T /ε) and H is a random universal hash function mapping to {0, 1}m , then (H(X1 ), . . . , H(XT )) has statistical difference at most ε from T uniform and independent elements of {0, 1}m . Thus, any event that would occur with some probability p under ideal hashing now occurs with p ...
Empirical Interpretations of Probability
... choose, there exists a process of measurement such that the result of applying that process of measurement to the table will yield a result that will (probably) differ from four by less than 6. It does not seem that the verification or falsification of assertions of probability are any more problema ...
... choose, there exists a process of measurement such that the result of applying that process of measurement to the table will yield a result that will (probably) differ from four by less than 6. It does not seem that the verification or falsification of assertions of probability are any more problema ...
The Applicability Problem for Chance
... that are (arguably) referred to by mature scientific theories.2 Philosophers disagree about which (if any) scientific theories are best interpreted as modeling chances but, partly for the sake of having a familiar toy example to work with, I’ll assume that the probabilities in weather reports model ...
... that are (arguably) referred to by mature scientific theories.2 Philosophers disagree about which (if any) scientific theories are best interpreted as modeling chances but, partly for the sake of having a familiar toy example to work with, I’ll assume that the probabilities in weather reports model ...
Raymond J. Solomonoff 1926-2009 - Computer Science
... Section on Information Theory, a forerunner of the IEEE Symposium on Information Theory. This partially used Chomsky’s paper [3] read at a Symposium on Information Theory held at MIT in September 1956. “An Inductive Inference Machine” already stressed training sequences and using previous solutions ...
... Section on Information Theory, a forerunner of the IEEE Symposium on Information Theory. This partially used Chomsky’s paper [3] read at a Symposium on Information Theory held at MIT in September 1956. “An Inductive Inference Machine” already stressed training sequences and using previous solutions ...
COHERENCE
... The first equality in I comes from the known chance and definition of utility; the second fom principle (1) page 9. The first equality in I1 comes from the definition of personal probability ofp and the subjects stated indifference; the second from principle (1) page 9. I and I1 are descriptions of ...
... The first equality in I comes from the known chance and definition of utility; the second fom principle (1) page 9. The first equality in I1 comes from the definition of personal probability ofp and the subjects stated indifference; the second from principle (1) page 9. I and I1 are descriptions of ...
Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?
... By looking for a trace in physics of the Boole-Vorobjev conclusion on nonexistence of probability one can find that this problem was intensively discussed, but in rather unusual form (at least from the mathematical viewpoint). During our conversations on the probabilistic structure of Bell’s inequal ...
... By looking for a trace in physics of the Boole-Vorobjev conclusion on nonexistence of probability one can find that this problem was intensively discussed, but in rather unusual form (at least from the mathematical viewpoint). During our conversations on the probabilistic structure of Bell’s inequal ...
Subjectivistic Interpretations of Probability
... that can be interpreted empirically, primarily on the ground that lacking this sort of prior information one could only assign prior probabilities subjectively, and that this subjectivity would therefore infect all of their results. (Here is a particularly clear example of the utter lack of communic ...
... that can be interpreted empirically, primarily on the ground that lacking this sort of prior information one could only assign prior probabilities subjectively, and that this subjectivity would therefore infect all of their results. (Here is a particularly clear example of the utter lack of communic ...
The Theory of Fuzzy Sets: Beliefs and Realities
... Glivenko – Cantelli theorem deals with establishing a limiting probability law from an empirical probability law. This theorem, like all other probabilistic formalisms, is true in the broader measure theoretic sense too of defining randomness. Unfortunately, at that juncture, the question of examine ...
... Glivenko – Cantelli theorem deals with establishing a limiting probability law from an empirical probability law. This theorem, like all other probabilistic formalisms, is true in the broader measure theoretic sense too of defining randomness. Unfortunately, at that juncture, the question of examine ...
PPT Chapter Six Discrete Probability Distributions
... X of 7’s rolled is recorded. (b) The 11 largest airlines had an on-time percentage of 84.7% in November, 2001 according to the Air Travel Consumer Report. In order to assess reasons for delays, an official with the FAA randomly selects flights until she finds 10 that were not on time. The number of ...
... X of 7’s rolled is recorded. (b) The 11 largest airlines had an on-time percentage of 84.7% in November, 2001 according to the Air Travel Consumer Report. In order to assess reasons for delays, an official with the FAA randomly selects flights until she finds 10 that were not on time. The number of ...
2.8 Probability and Odds
... Use the circle graph below showing the responses of 250 college students to a survey asking “Which factor is most likely to influence your job choice after graduation?” If you were to ask a randomly chosen college student this question, what is the experimental probability that the student would say ...
... Use the circle graph below showing the responses of 250 college students to a survey asking “Which factor is most likely to influence your job choice after graduation?” If you were to ask a randomly chosen college student this question, what is the experimental probability that the student would say ...
Objective probability-like things with and without objective
... probability, is that there is no such property of an event as its “probability”. If there is any reason to use this word, “probability” is merely a collective term: its meaning varies from context to context. Moreover, these contextdependent meanings reduce the concept of “probability” to ordinary p ...
... probability, is that there is no such property of an event as its “probability”. If there is any reason to use this word, “probability” is merely a collective term: its meaning varies from context to context. Moreover, these contextdependent meanings reduce the concept of “probability” to ordinary p ...
Applications of Mathematics 12
... 2. Learn to clear the lists from your memory after you are done 3. use the binompdf function to determine the probability distribution 4. Determine the probability of a. EXACTLY a certain number binompdf(n, p x) b. At MOST a certain number ...
... 2. Learn to clear the lists from your memory after you are done 3. use the binompdf function to determine the probability distribution 4. Determine the probability of a. EXACTLY a certain number binompdf(n, p x) b. At MOST a certain number ...
Study Materials
... Introduction:When a Fair coin is tossed, the face shown up is head or tail. Before tossing the coin, it is not possible to predict which face shows up. Such experiments where the outcomes cannot be predicted with certainty are called Random experiments. Random experiment and phenomena are the heart ...
... Introduction:When a Fair coin is tossed, the face shown up is head or tail. Before tossing the coin, it is not possible to predict which face shows up. Such experiments where the outcomes cannot be predicted with certainty are called Random experiments. Random experiment and phenomena are the heart ...
A Philosopher`s Guide to Probability
... objective notion of probability, heedless of anyone‘s beliefs. It is also the philosophical position that lies in the background of the classical Fisher/Neyman-Pearson approach that is used in most statistics textbooks. Frequentism does, however, face some major objections. For example, a coin that ...
... objective notion of probability, heedless of anyone‘s beliefs. It is also the philosophical position that lies in the background of the classical Fisher/Neyman-Pearson approach that is used in most statistics textbooks. Frequentism does, however, face some major objections. For example, a coin that ...
Objective probability-like things with and without - Philsci
... probability, is that there is no such property of an event as its “probability”. If there is any reason to use this word, “probability” is merely a collective term: its meaning varies from context to context. Moreover, these contextdependent meanings reduce the concept of “probability” to ordinary p ...
... probability, is that there is no such property of an event as its “probability”. If there is any reason to use this word, “probability” is merely a collective term: its meaning varies from context to context. Moreover, these contextdependent meanings reduce the concept of “probability” to ordinary p ...
Probability and Inference
... Based on this poll, can we compute the probability that a particular candidate will win? Some might (wrongly) look at the poll and suppose that Nader’s chance of winning is 6%: after all, he seems to have 6% of the electorate behind him. In fact, given the profile in Table 2, the chance of Nader win ...
... Based on this poll, can we compute the probability that a particular candidate will win? Some might (wrongly) look at the poll and suppose that Nader’s chance of winning is 6%: after all, he seems to have 6% of the electorate behind him. In fact, given the profile in Table 2, the chance of Nader win ...
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.