Math modeling unit and activity –Conditional Probability
... the free throw, Memphis brings the ball down the court and attempts a three-point shot but they are fouled. The clock is now at zero and the Memphis player will shoot three free throws at one point for each shot he makes. The students will decide (using probability calculations and their own assumpt ...
... the free throw, Memphis brings the ball down the court and attempts a three-point shot but they are fouled. The clock is now at zero and the Memphis player will shoot three free throws at one point for each shot he makes. The students will decide (using probability calculations and their own assumpt ...
Q1. A lot consists of 144 ball pens of which... buy a pen if it is good, but will not...
... Q16. Tickets numbered from 1 to 20 are mixed up together and then a ticket is drown at random. What is the probability that the ticket has a number which is a multiple of 3 or 7. Q17. It is known that a box of 600 electric bulbs contains 12 defective bulbs. One bulb is taken out at random from this ...
... Q16. Tickets numbered from 1 to 20 are mixed up together and then a ticket is drown at random. What is the probability that the ticket has a number which is a multiple of 3 or 7. Q17. It is known that a box of 600 electric bulbs contains 12 defective bulbs. One bulb is taken out at random from this ...
Binomial Probabilities
... experiment n times. For example, we want to understand how to calculate the following probabilities. (1) What is the probability that I get at least 3 heads if I toss a fair coin 5 times? (2) What is the probability that if I throw a die three times, two out of those three throws will be less than o ...
... experiment n times. For example, we want to understand how to calculate the following probabilities. (1) What is the probability that I get at least 3 heads if I toss a fair coin 5 times? (2) What is the probability that if I throw a die three times, two out of those three throws will be less than o ...
Statistical Significance and the Burden of Persuasion
... statistical evidence in these proceedings, they are not always certain of how to weigh the evidence or whether they should, or must, rely on the standards for proof that scientists apply in evaluating statistical hypotheses. Two decisions of the Supreme Court illustrate this uncertainty. In Caslaned ...
... statistical evidence in these proceedings, they are not always certain of how to weigh the evidence or whether they should, or must, rely on the standards for proof that scientists apply in evaluating statistical hypotheses. Two decisions of the Supreme Court illustrate this uncertainty. In Caslaned ...
Poisson Probability Distributions
... time, volume, and so forth. This distribution applies to accident rates, arrival times, defect rates, the incidents of bacteria in the air, smoke alarms, and many other areas of everyday life. As with a binomial distribution, we can assume only two outcomes, a particular event occurs (success) or do ...
... time, volume, and so forth. This distribution applies to accident rates, arrival times, defect rates, the incidents of bacteria in the air, smoke alarms, and many other areas of everyday life. As with a binomial distribution, we can assume only two outcomes, a particular event occurs (success) or do ...
1 Bayesian models of perceptual organization Jacob Feldman Dept
... The use of Bayesian inference as a model for perception rests on two basic ideas. The first, just mentioned, is the basic idea of inverse probability as a general method for determining belief under conditions of uncertainty. Bayesian inference allows us to quantify the degree to which different sce ...
... The use of Bayesian inference as a model for perception rests on two basic ideas. The first, just mentioned, is the basic idea of inverse probability as a general method for determining belief under conditions of uncertainty. Bayesian inference allows us to quantify the degree to which different sce ...
UNCERTAINTY THEORIES: A UNIFIED VIEW
... • Find representations that – Distinguish between uncertainty due to variability from uncertainty due to lack of knowledge or missing information – Reflect partial knowledge faithfully – Are more expressive that pure set representations – Allows for addressing the same problems as probability. ...
... • Find representations that – Distinguish between uncertainty due to variability from uncertainty due to lack of knowledge or missing information – Reflect partial knowledge faithfully – Are more expressive that pure set representations – Allows for addressing the same problems as probability. ...
Probability
... This is bizarre! She says if you get it right she will release you from “the game” for the night. But if you are wrong, she will put you one step closer to being stuck forever in . . . ...
... This is bizarre! She says if you get it right she will release you from “the game” for the night. But if you are wrong, she will put you one step closer to being stuck forever in . . . ...
ExamView - Binomial Probability Problem Set
... Find the probability of the Raiders winning: (1) exactly 4 out of five games (2) at most 4 out of five games (3) exactly 4 out of five games if they have already won the first two games ...
... Find the probability of the Raiders winning: (1) exactly 4 out of five games (2) at most 4 out of five games (3) exactly 4 out of five games if they have already won the first two games ...
A Minimal Extension of Bayesian Decision Theory
... a subjective probability can meaningfully be assigned—is defined to be closed under complements and countable unions. We deviate slightly from the standard definition in allowing M to be empty, noting that M = ∅ implies {∅, B} ⊆ M. In proving theorems, we assume that B is a finite set, so that proving ...
... a subjective probability can meaningfully be assigned—is defined to be closed under complements and countable unions. We deviate slightly from the standard definition in allowing M to be empty, noting that M = ∅ implies {∅, B} ⊆ M. In proving theorems, we assume that B is a finite set, so that proving ...
distributions
... d. Find the probability that the rating given is 3 or less. Note: When we find the probability that a variable is less than or equal to some value it is called a cumulative probability. To find it, we add probabilities for all values up to and including that point. ...
... d. Find the probability that the rating given is 3 or less. Note: When we find the probability that a variable is less than or equal to some value it is called a cumulative probability. To find it, we add probabilities for all values up to and including that point. ...
6.4Bayesian Classification
... attribute-value pair, per class (i.e., per Ci , for i = 1, . . . , m). In Example 6.4, we have two classes (m = 2), namely buys computer = yes and buys computer = no. Therefore, for the attribute-value pair student = yes of X, say, we need two counts—the number of customers who are students and for ...
... attribute-value pair, per class (i.e., per Ci , for i = 1, . . . , m). In Example 6.4, we have two classes (m = 2), namely buys computer = yes and buys computer = no. Therefore, for the attribute-value pair student = yes of X, say, we need two counts—the number of customers who are students and for ...
Lecture 10, January 28, 2004
... invoices, so after the first pick (with error), we have only 23 invoices left. And the among those 23 invoices only 3 invoices could have errors. So, the probability of the second event (picking an invoice with error in second draw) is 3/23. The probability that both will contain error is 4/24 X 3/2 ...
... invoices, so after the first pick (with error), we have only 23 invoices left. And the among those 23 invoices only 3 invoices could have errors. So, the probability of the second event (picking an invoice with error in second draw) is 3/23. The probability that both will contain error is 4/24 X 3/2 ...
Ch6 Probability Review Name: Government data give the following
... 5. Choose an American adult at random. The probability that you choose a woman is 0.52. The probability that the person you choose has never married is 0.24. The probability that you choose a woman who has never married is 0.11. The probability that the person you choose is either a woman or never m ...
... 5. Choose an American adult at random. The probability that you choose a woman is 0.52. The probability that the person you choose has never married is 0.24. The probability that you choose a woman who has never married is 0.11. The probability that the person you choose is either a woman or never m ...
Chapter10slides
... different methods for the same event are inconsistent, which method should be taken as the true index of degree of belief? One way to answer this question is to use a single method of assessing subjective probability that is most consistent with itself. (+) ...
... different methods for the same event are inconsistent, which method should be taken as the true index of degree of belief? One way to answer this question is to use a single method of assessing subjective probability that is most consistent with itself. (+) ...
Derivation of Binomial Probability Formula
... work with the case in which the first two peas are yellow and the others are green. (Note: we will assume that all non-yellow peas are green even though other colors may exist; the important point to make is that we are concerned with only two actual possibilities of pea colors for our experiment, y ...
... work with the case in which the first two peas are yellow and the others are green. (Note: we will assume that all non-yellow peas are green even though other colors may exist; the important point to make is that we are concerned with only two actual possibilities of pea colors for our experiment, y ...
Probability: What Chance Do You Have?
... in the discussion of probability even though the odds of an outcome are different from the probability of the same outcome. There are two different types of odds: Odds against an outcome Odds in favor of an outcome ...
... in the discussion of probability even though the odds of an outcome are different from the probability of the same outcome. There are two different types of odds: Odds against an outcome Odds in favor of an outcome ...
Probability Rules
... 14) If two coins are tossed, what is the probability of getting one head and one tail? 15) A fair die and a fair coin are tossed. What is the probability of obtaining an 8 on the die and a head on the coin? 16) If a fair coin is tossed, what is the probability of getting three tails? 17) At a certai ...
... 14) If two coins are tossed, what is the probability of getting one head and one tail? 15) A fair die and a fair coin are tossed. What is the probability of obtaining an 8 on the die and a head on the coin? 16) If a fair coin is tossed, what is the probability of getting three tails? 17) At a certai ...
Probability Theory
... Pottery dice have been found in Egyptian tombs built before 2000 B.C, and by the time Greek civilizations were in full flower, dice were everywhere. Loaded dice have also been found from antiquity. While mastering the mathematics of probability would prove to be a formidable task for our ancestors, ...
... Pottery dice have been found in Egyptian tombs built before 2000 B.C, and by the time Greek civilizations were in full flower, dice were everywhere. Loaded dice have also been found from antiquity. While mastering the mathematics of probability would prove to be a formidable task for our ancestors, ...
A Syntactic Justification of Occam`s Razor
... Occam’s razor states “pick the simplest hypothesis consistent with data” We agree, but for a different reason. Restatement. Pick the function that is represented most frequently (i.e. belongs to the largest equivalence class). Occam’s razor is concerned with probability, and we present a simple coun ...
... Occam’s razor states “pick the simplest hypothesis consistent with data” We agree, but for a different reason. Restatement. Pick the function that is represented most frequently (i.e. belongs to the largest equivalence class). Occam’s razor is concerned with probability, and we present a simple coun ...
Frequentist vs Bayesian statistics --- a non
... Frequentists define probability as the long-run frequency of a certain measurement or observation. The frequentist says that there is a single truth and our measurement samples noisy instances of this truth. The more data we collect, the better we can pinpoint the truth. The archetypal example is th ...
... Frequentists define probability as the long-run frequency of a certain measurement or observation. The frequentist says that there is a single truth and our measurement samples noisy instances of this truth. The more data we collect, the better we can pinpoint the truth. The archetypal example is th ...
BINOMIAL THEOREM
... 1. Derive the binomial distribution by considering the sum of the outcomes xi ; i = 1, . . . , n of n independent trials where P (xi = 1) = p and P (xi = 0) = 1 − p for all i. A particle moves between adjacent nodes of a diagonal lattice. The nodes correspond to the integer points (x, y) for which x ...
... 1. Derive the binomial distribution by considering the sum of the outcomes xi ; i = 1, . . . , n of n independent trials where P (xi = 1) = p and P (xi = 0) = 1 − p for all i. A particle moves between adjacent nodes of a diagonal lattice. The nodes correspond to the integer points (x, y) for which x ...
INDUCTION
... The notion of causation is to some extent ambiguous. When we say that A is the cause of B or a cause of B, we can mean that A is a necessary condition of B, that A is a sufficient condition of B, or that A is both a necessary and sufficient condition of B. There are deep philosophical difficulties c ...
... The notion of causation is to some extent ambiguous. When we say that A is the cause of B or a cause of B, we can mean that A is a necessary condition of B, that A is a sufficient condition of B, or that A is both a necessary and sufficient condition of B. There are deep philosophical difficulties c ...
Computation of the Probability of Initial Substring Generation by
... Probabilistic methods have been shown most effective in automatic speech recognition. Recognition (actually transcription) of natural unrestricted speech requires a "language model" that attaches probabilities to the production of all possible strings of words (Bahl et al. 1983). Consequently, if we ...
... Probabilistic methods have been shown most effective in automatic speech recognition. Recognition (actually transcription) of natural unrestricted speech requires a "language model" that attaches probabilities to the production of all possible strings of words (Bahl et al. 1983). Consequently, if we ...
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.