DOC - MathsGeeks
... A tree diagram is a way of calculating probabilities when two events are combined. Example (worked examination question): Helen tries to win a coconut at the fair. She throws a ball at a coconut. If she knocks the coconut off the standard she wins the coconut. Helen has two throws. The probability t ...
... A tree diagram is a way of calculating probabilities when two events are combined. Example (worked examination question): Helen tries to win a coconut at the fair. She throws a ball at a coconut. If she knocks the coconut off the standard she wins the coconut. Helen has two throws. The probability t ...
Probability Quiz
... run, on the average, a head turns up 3 times in 10 tosses. If this biased coin is tossed simultaneously with an unbiased coin, what is the probability that both will fall as heads? ...
... run, on the average, a head turns up 3 times in 10 tosses. If this biased coin is tossed simultaneously with an unbiased coin, what is the probability that both will fall as heads? ...
Conditional Probability
... Students at the University of New Harmony received 10,000 course grades last semester ...
... Students at the University of New Harmony received 10,000 course grades last semester ...
Representing Variable Source Credibility in Intelligence Analysis
... with node ‘Cred 2’ which corresponds to our belief in the credibility of our HUMINT source. This is explained by the lack of dry run evidence entered in Fig 5 which shifts the credibility distribution of the HUMINT source towards lower levels. At first, an analyst may not expect a credibility assess ...
... with node ‘Cred 2’ which corresponds to our belief in the credibility of our HUMINT source. This is explained by the lack of dry run evidence entered in Fig 5 which shifts the credibility distribution of the HUMINT source towards lower levels. At first, an analyst may not expect a credibility assess ...
Section 7B: Combining Probabilities
... Example. Suppose you roll a fair six-sided die twice. What is the probability that you will get a 2 on the first roll, and then an odd number on the second roll? ...
... Example. Suppose you roll a fair six-sided die twice. What is the probability that you will get a 2 on the first roll, and then an odd number on the second roll? ...
Reasoning with Probabilities
... Although this course has an interdisciplinary goal aiming to introduce students from one discipline to methods in another, and although the course is self-contained with many basic concepts of probability theory (e.g., measure spaces) being explained, it is considered an advanced course because it f ...
... Although this course has an interdisciplinary goal aiming to introduce students from one discipline to methods in another, and although the course is self-contained with many basic concepts of probability theory (e.g., measure spaces) being explained, it is considered an advanced course because it f ...
Section 1: Basic Probability Concepts
... If S has finitely many points, say S = {a1 , a2 , . . . , ak }, then a probability function P is uniform if P[ai ] = k1 . This says that each outcome is equally (or uniformly) likely to occur. When rolling a fair six-sided die, each side is equally likely to come up. In fact, the probability of get ...
... If S has finitely many points, say S = {a1 , a2 , . . . , ak }, then a probability function P is uniform if P[ai ] = k1 . This says that each outcome is equally (or uniformly) likely to occur. When rolling a fair six-sided die, each side is equally likely to come up. In fact, the probability of get ...
Bayesian, Likelihood, and Frequentist Approaches to Statistics
... from which urn to withdraw a ball was made at random, with each urn being given an equal chance of being chosen. I did specify that the ball was chosen from the urn at random. The net result of this is that although some of the probabilities for this problem are well defined, for example the probabi ...
... from which urn to withdraw a ball was made at random, with each urn being given an equal chance of being chosen. I did specify that the ball was chosen from the urn at random. The net result of this is that although some of the probabilities for this problem are well defined, for example the probabi ...
Bayesian Probability
... First, inductive probability isn’t the same thing as degree of belief. To see this, suppose I claim that a theory H is probable in view of the available evidence. The reference to evidence shows that this is a statement of inductive probability. If inductive probability were degree of belief then I ...
... First, inductive probability isn’t the same thing as degree of belief. To see this, suppose I claim that a theory H is probable in view of the available evidence. The reference to evidence shows that this is a statement of inductive probability. If inductive probability were degree of belief then I ...
Section 5.1 Randomness, Probability, and Simulation The Idea of
... Almost everyone says that HTHTTH is more probable, because TTTHHH does not “look random.” In fact, both are equally likely. That heads and tails are equally probable says only that about half of a very long sequence of tosses will be heads. It doesn’t say that heads and tails must come close to alte ...
... Almost everyone says that HTHTTH is more probable, because TTTHHH does not “look random.” In fact, both are equally likely. That heads and tails are equally probable says only that about half of a very long sequence of tosses will be heads. It doesn’t say that heads and tails must come close to alte ...
Bayesian Belief Network
... • It is common to think of Bayes’ rule in terms of updating our belief about a hypothesis A in the light of new evidence B. • Specifically, our posterior belief P(A|B) is calculated by multiplying our prior belief P(A) by the likelihood P(B|A) that B will occur if A is true. • The power of Bayes’ ru ...
... • It is common to think of Bayes’ rule in terms of updating our belief about a hypothesis A in the light of new evidence B. • Specifically, our posterior belief P(A|B) is calculated by multiplying our prior belief P(A) by the likelihood P(B|A) that B will occur if A is true. • The power of Bayes’ ru ...
Gain Confidence with Probability: The Two-Way Table 1
... The symbol stands for the “union” and represent the “or” condition, while the symbol stands for “intersection” and represents the “and” condition. Often the symbol “ | ” is used to represent “given that”. P(G | H) represents the probability of G given that H has occurred. Convert the following l ...
... The symbol stands for the “union” and represent the “or” condition, while the symbol stands for “intersection” and represents the “and” condition. Often the symbol “ | ” is used to represent “given that”. P(G | H) represents the probability of G given that H has occurred. Convert the following l ...
prob_distr_disc
... 1. In each part, indicate, (1) whether the variable is discrete or continuous AND (2) whether it is binomial or not AND (3) if it is binomial, give values for n and p. a. Number of times a “head” comes up in 10 flips of a coin 1. Discrete or continuous 2. Binomial yes or no 3. If Binomial what is n ...
... 1. In each part, indicate, (1) whether the variable is discrete or continuous AND (2) whether it is binomial or not AND (3) if it is binomial, give values for n and p. a. Number of times a “head” comes up in 10 flips of a coin 1. Discrete or continuous 2. Binomial yes or no 3. If Binomial what is n ...
Typical Test Problems (with solutions)
... The conventional solution is p= C4,2C6,2/C6,4=0.429. Trying to be silly, we can also use a Binomial formula assuming that the probabilities are 3/5 and 2/5: p = C4,2(2/5)2(3/5)2= 0.346. This time the difference is significant. In addition, we can now understand the source of the problem, The Binomi ...
... The conventional solution is p= C4,2C6,2/C6,4=0.429. Trying to be silly, we can also use a Binomial formula assuming that the probabilities are 3/5 and 2/5: p = C4,2(2/5)2(3/5)2= 0.346. This time the difference is significant. In addition, we can now understand the source of the problem, The Binomi ...
Conditional Probability and Independence
... Students at the University of New Harmony received 10,000 course grades last semester ...
... Students at the University of New Harmony received 10,000 course grades last semester ...
Ch5 Study Questions File
... STAT201 Study Questions on Chapter 5 15th ed. Q. 19) Suppose two events A and B are mutually exclusive. What is the probability of their joint occurence? When two events are mutually exclusive it means that if one occurs the other event cannot occur at the same time. Therefore, the probability of th ...
... STAT201 Study Questions on Chapter 5 15th ed. Q. 19) Suppose two events A and B are mutually exclusive. What is the probability of their joint occurence? When two events are mutually exclusive it means that if one occurs the other event cannot occur at the same time. Therefore, the probability of th ...
An Evolutionary Argument Against Naturalism
... opinion" by Rob Cummins (Meaning and Mental Representation); if you accept materialism re minds, it's hard to see any alternative. (c) A third possibility: it could be that belief cause behavior by way of content but is maladaptive. Again, low. (d) the beliefs or our hypothetical creatures cause the ...
... opinion" by Rob Cummins (Meaning and Mental Representation); if you accept materialism re minds, it's hard to see any alternative. (c) A third possibility: it could be that belief cause behavior by way of content but is maladaptive. Again, low. (d) the beliefs or our hypothetical creatures cause the ...
Example 3, Pg. 253, #7
... In the above definition for the addition rule, I claim that the chances can be added if two events are mutually exclusive. What if two events are not mutually exclusive? In this case we cannot add the chances because our sum will be too big. Let’s see why, through an example. Example Find the probab ...
... In the above definition for the addition rule, I claim that the chances can be added if two events are mutually exclusive. What if two events are not mutually exclusive? In this case we cannot add the chances because our sum will be too big. Let’s see why, through an example. Example Find the probab ...
4 Conditional Probability - Notes
... Experiment Yourself – This is a famous problem. On the original show, Let’s Make a Deal, contestants were given a choice of 3 curtains. They chose one and the host, Monty Hall, would show them a ZONK! that was behind one of the doors that they did not choose. They were then given the opportunity to ...
... Experiment Yourself – This is a famous problem. On the original show, Let’s Make a Deal, contestants were given a choice of 3 curtains. They chose one and the host, Monty Hall, would show them a ZONK! that was behind one of the doors that they did not choose. They were then given the opportunity to ...
Discovery or fluke: STATISTICS IN PARTICLE PHYSICS
... A big issue in Bayesian analysis is what functional form to use for the prior, especially in situations where little is known in advance about the parameter being sought. Take, for example, the mass Ml of the lightest neutrino. The argument that the prior function should simply be a constant so as n ...
... A big issue in Bayesian analysis is what functional form to use for the prior, especially in situations where little is known in advance about the parameter being sought. Take, for example, the mass Ml of the lightest neutrino. The argument that the prior function should simply be a constant so as n ...
Form groups of two or three and discuss the following questions
... the following in small groups of 3-4 persons. Write down your reasoning in each case:(i) how the second number in the “Survivorship” column is derived from those in the “Age < 1” row; (ii) how to calculate the third and subsequent numbers in the “Survivorship” column. Note that the solution will be ...
... the following in small groups of 3-4 persons. Write down your reasoning in each case:(i) how the second number in the “Survivorship” column is derived from those in the “Age < 1” row; (ii) how to calculate the third and subsequent numbers in the “Survivorship” column. Note that the solution will be ...
`USING PROBABILITY TO DESCRIBE SITUATIONS`
... Using probability to describe situations Probability is measured on a scale of 0 to1 If an event is certain to happen then it is said to have a probability of 1 or 100%. If an event is certain not to happen then it is said to have a probability of 0 or 0%. If an event may or may not happen then it w ...
... Using probability to describe situations Probability is measured on a scale of 0 to1 If an event is certain to happen then it is said to have a probability of 1 or 100%. If an event is certain not to happen then it is said to have a probability of 0 or 0%. If an event may or may not happen then it w ...
Introduction to Probability Exercise sheet 3 Exercise 1. 5 cards
... A coin is tossed. If it comes out heads, we toss die A twice, and if the coin comes out tails, we toss die B twice. (a) The coin is a fair coin (probability 1/2 for each side). Given that the outcome of the die is twice blue, what is the probability that we tossed die A? (b) The coin is an unfair co ...
... A coin is tossed. If it comes out heads, we toss die A twice, and if the coin comes out tails, we toss die B twice. (a) The coin is a fair coin (probability 1/2 for each side). Given that the outcome of the die is twice blue, what is the probability that we tossed die A? (b) The coin is an unfair co ...
union
... This will sort the day in increasing order; scroll through the list to see duplicate birthdays. Repeat many times. • The following short program can be used to find the probability of at least 2 people in a group of n people having the same birthday : Prompt N : 1- (prod((seq((366-X)/365, X, 1, N, 1 ...
... This will sort the day in increasing order; scroll through the list to see duplicate birthdays. Repeat many times. • The following short program can be used to find the probability of at least 2 people in a group of n people having the same birthday : Prompt N : 1- (prod((seq((366-X)/365, X, 1, N, 1 ...
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.