Probability - Vicki Martinez
... • Suppose you had cubes in a bag. Three are red, 2 are blue, and 2 are green. • Without looking, you reach in and pull out one cube. • What is the probability that the cube will be ...
... • Suppose you had cubes in a bag. Three are red, 2 are blue, and 2 are green. • Without looking, you reach in and pull out one cube. • What is the probability that the cube will be ...
Statistics
... Theorem 13: If A1 , . . . , An are independent then also Ac1 , . . . , Acm , Am+1 , . . . , An are independent for any 0 < m ≤ n. Example 25: Label the statements true or false. (i) The target is to be hit at least once. In three independent shots at the target (instead of one shot) you triple the c ...
... Theorem 13: If A1 , . . . , An are independent then also Ac1 , . . . , Acm , Am+1 , . . . , An are independent for any 0 < m ≤ n. Example 25: Label the statements true or false. (i) The target is to be hit at least once. In three independent shots at the target (instead of one shot) you triple the c ...
Applications of Mathematics 12
... 1. Recall from chapter one: a Binomial experiment satisfies the following four conditions: 1. The experiment consists of n identical trials. 2. Each trial results in one of the two outcomes, called success and failure. 3. The probability of success, denoted p , remains the same from trial to trial. ...
... 1. Recall from chapter one: a Binomial experiment satisfies the following four conditions: 1. The experiment consists of n identical trials. 2. Each trial results in one of the two outcomes, called success and failure. 3. The probability of success, denoted p , remains the same from trial to trial. ...
Chapter 13. What Are the Chances?
... put on that first draw: it must be an apple. To answer the question, think of how things changed. ...
... put on that first draw: it must be an apple. To answer the question, think of how things changed. ...
Reduction(6).pdf
... In order to introduce the concept of the payoff for accepting a hypothesis, consider the special case in which h1 and h2 postulate that the probability function over the possible states of the experimental situation are λ1 and λ2, respectively. Suppose that the observed outcome is HT, and a decisio ...
... In order to introduce the concept of the payoff for accepting a hypothesis, consider the special case in which h1 and h2 postulate that the probability function over the possible states of the experimental situation are λ1 and λ2, respectively. Suppose that the observed outcome is HT, and a decisio ...
What Conditional Probability Also Could Not Be
... offers in the spirit of my argument from vague probabilities is this: “Consider two infinitely thin darts thrown at the real line, with independent uniform probability distributions over the interval [0, 100]… Given that the first dart hits a large value, what is the probability that the second dar ...
... offers in the spirit of my argument from vague probabilities is this: “Consider two infinitely thin darts thrown at the real line, with independent uniform probability distributions over the interval [0, 100]… Given that the first dart hits a large value, what is the probability that the second dar ...
Lecture 1
... about them. The notion of an experiment assumes a set of repeatable conditions that allow any number of identical repetitions. When an experiment is performed under these conditions, certain elementary events i occur in different but completely uncertain ways. We can assign nonnegative number P(i ...
... about them. The notion of an experiment assumes a set of repeatable conditions that allow any number of identical repetitions. When an experiment is performed under these conditions, certain elementary events i occur in different but completely uncertain ways. We can assign nonnegative number P(i ...
IGE104-Lecture9
... We define an event as one or more possible outcomes that all have the same property of interest Coin A ...
... We define an event as one or more possible outcomes that all have the same property of interest Coin A ...
Chapter 5 - Elementary Probability Theory Historical Background
... being the “father” of probability theory. In the twentieth century a coherent mathematical theory of probability was developed through people such as Chebyshev, Markov, and Kolmogorov. Probability The study of probability is concerned with random phenomena. Even though we cannot be certain whether a ...
... being the “father” of probability theory. In the twentieth century a coherent mathematical theory of probability was developed through people such as Chebyshev, Markov, and Kolmogorov. Probability The study of probability is concerned with random phenomena. Even though we cannot be certain whether a ...
Artificial Intelligence, Lecture 6.1, Page 1
... Probability is an agent’s measure of belief in some proposition — subjective probability. An agent’s belief depends on its prior assumptions and what the agent observes. ...
... Probability is an agent’s measure of belief in some proposition — subjective probability. An agent’s belief depends on its prior assumptions and what the agent observes. ...
A Joint Characterization of Belief Revision Rules
... probability of some event given another, or, more generally, a new distribution of some random variable given another random variable, for instance a new distribution of the weather given the weather forecast, or of GDP given in‡ation (e.g., Bradley 2005, 2007, Douven and Romeijn 2012).2 An excellen ...
... probability of some event given another, or, more generally, a new distribution of some random variable given another random variable, for instance a new distribution of the weather given the weather forecast, or of GDP given in‡ation (e.g., Bradley 2005, 2007, Douven and Romeijn 2012).2 An excellen ...
9.8 Exercises
... Probability and statistics are two closely related branches of mathematics. They apply to all science and engineering fields, sociology, business, education, insurance, and many others. For this reason, we devote all subsequent modules to this topic. In some cases, measurements of various parameters ...
... Probability and statistics are two closely related branches of mathematics. They apply to all science and engineering fields, sociology, business, education, insurance, and many others. For this reason, we devote all subsequent modules to this topic. In some cases, measurements of various parameters ...
Is it a Crime to Belong to a Reference Class?
... in the Shonubi case so that the total quantity of drugs should include all eight of Shonubi's drug-smuggling episodes. It was estimated that the total quantity of heroin that Shonubi carried into the USA on his eight trips was 427.468=3,419.2 grams. This was above the crucial 3,000 gram threshold an ...
... in the Shonubi case so that the total quantity of drugs should include all eight of Shonubi's drug-smuggling episodes. It was estimated that the total quantity of heroin that Shonubi carried into the USA on his eight trips was 427.468=3,419.2 grams. This was above the crucial 3,000 gram threshold an ...
Math SCO G1 and G2
... How do you calculate theoretical probability of tossing a 4 using a regular die? Determine how many times a particular outcome (possibility) exists in that situation. The number 4 is found once on the die. So the numerator needed for the theoretical probability is 1 since there is only 1 four ...
... How do you calculate theoretical probability of tossing a 4 using a regular die? Determine how many times a particular outcome (possibility) exists in that situation. The number 4 is found once on the die. So the numerator needed for the theoretical probability is 1 since there is only 1 four ...
Probability and Random Processes Measure
... “Borel measurable function” more general than “continuous function” • f Borel measurable ⇒ f Lebesgue measurable (but not vice ...
... “Borel measurable function” more general than “continuous function” • f Borel measurable ⇒ f Lebesgue measurable (but not vice ...
The argument from so many arguments
... cases in which there are multiple items of independent evidence. I will use this Bayesian model to evaluate the strength of evidence for theism if, as Plantinga claims, there are two dozen or so arguments for theism.1 Formal models are justified by their clarity, precision, and usefulness, even thou ...
... cases in which there are multiple items of independent evidence. I will use this Bayesian model to evaluate the strength of evidence for theism if, as Plantinga claims, there are two dozen or so arguments for theism.1 Formal models are justified by their clarity, precision, and usefulness, even thou ...
Introduction to Probability I
... Bayesian (subjective) probability - reflects a person’s opinion about how likely an event is to occur, it represents the person’s strength of belief – Prior beliefs are updated using observed data – Valid in situations where long run relative frequency is not applicable ...
... Bayesian (subjective) probability - reflects a person’s opinion about how likely an event is to occur, it represents the person’s strength of belief – Prior beliefs are updated using observed data – Valid in situations where long run relative frequency is not applicable ...
Propensities Lars-Göran Johansson
... normalised state functions in the same Hilbert space fulfils Kolmogorov’s axioms for a probability measure, and these scalar products, expressing transition probabilities, provide the required propensities. Let’s imagine that we have a physical system, isolated from the rest of the world. Its state ...
... normalised state functions in the same Hilbert space fulfils Kolmogorov’s axioms for a probability measure, and these scalar products, expressing transition probabilities, provide the required propensities. Let’s imagine that we have a physical system, isolated from the rest of the world. Its state ...
How Many Marbles?
... answer 1/2, because there are two marbles but only one is blue.] 4. Put all 12 marbles in the bag and ask: “What is the probability that I will draw a red one?” [Students should answer 3/12, which will reduce to 1/4, because there are three red marbles in a bag of ...
... answer 1/2, because there are two marbles but only one is blue.] 4. Put all 12 marbles in the bag and ask: “What is the probability that I will draw a red one?” [Students should answer 3/12, which will reduce to 1/4, because there are three red marbles in a bag of ...
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 ...
possible numbers total possible numbers even . . . . 2 1 6 3 =
... There are a couple of things to note about this experiment. Choosing a pairs of socks from the drawer, replacing it, and then choosing a pair again from the same drawer is a compound event (a compound event consists of two or more simple events.) Since the first pair was replaced, choosing a red pai ...
... There are a couple of things to note about this experiment. Choosing a pairs of socks from the drawer, replacing it, and then choosing a pair again from the same drawer is a compound event (a compound event consists of two or more simple events.) Since the first pair was replaced, choosing a red pai ...
Dempster–Shafer theory
The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. First introduced by Arthur P. Dempster in the context of statistical inference, the theory was later developed by Glenn Shafer into a general framework for modeling epistemic uncertainty - a mathematical theory of evidence. The theory allows one to combine evidence from different sources and arrive at a degree of belief (represented by a mathematical object called belief function) that takes into account all the available evidence.In a narrow sense, the term Dempster–Shafer theory refers to the original conception of the theory by Dempster and Shafer. However, it is more common to use the term in the wider sense of the same general approach, as adapted to specific kinds of situations. In particular, many authors have proposed different rules for combining evidence, often with a view to handling conflicts in evidence better. The early contributions have also been the starting points of many important developments, including the Transferable Belief Model and the Theory of Hints.