probability literacy, statistical literacy, adult numeracy, quantitative
... uncertainty. Decisions have several subtypes, among them are planning (the identification, design, and choice of an optimal way to use resources; Secretary of Labor’s Commission on Achieving Necessary Skills, 1991) and choice (the selection of one or more options from given alternatives; Clemen & Gr ...
... uncertainty. Decisions have several subtypes, among them are planning (the identification, design, and choice of an optimal way to use resources; Secretary of Labor’s Commission on Achieving Necessary Skills, 1991) and choice (the selection of one or more options from given alternatives; Clemen & Gr ...
Solutions: AMC Prep for ACHS: Counting and Probability
... Tina randomly selects two distinct numbers from the set {1, 2, 3, 4, 5}, and Sergio randomly selects a number from the set {1, 2, . . . , 10}. What is the probability that Sergio’s number is larger than the sum of the two numbers chosen by Tina? There are ten ways for Tina to select a pair of number ...
... Tina randomly selects two distinct numbers from the set {1, 2, 3, 4, 5}, and Sergio randomly selects a number from the set {1, 2, . . . , 10}. What is the probability that Sergio’s number is larger than the sum of the two numbers chosen by Tina? There are ten ways for Tina to select a pair of number ...
Title of slide - WebHome < PP/Public < RHUL Physics
... Bayes’ theorem has an “if-then” character: If your prior probabilities were p (H), then it says how these probabilities should change in the light of the data. No general prescription for priors (subjective!) G. Cowan ...
... Bayes’ theorem has an “if-then” character: If your prior probabilities were p (H), then it says how these probabilities should change in the light of the data. No general prescription for priors (subjective!) G. Cowan ...
Weighted Sets of Probabilities and Minimax Weighted Expected
... states where there is exactly one broken cake to be equally probable, and take the remaining states to have probability 0; if the stairs are fifteen feet high, we can take all of the C(1000, 10) states where there are exactly ten broken cakes to be equally probable, and take the remaining states to ...
... states where there is exactly one broken cake to be equally probable, and take the remaining states to have probability 0; if the stairs are fifteen feet high, we can take all of the C(1000, 10) states where there are exactly ten broken cakes to be equally probable, and take the remaining states to ...
Exercise Problems: Information Theory and Coding
... = −(1 − ǫ) log(0.5(1 − ǫ)) − ǫ log(0.5ǫ) = (1 − ǫ) − (1 − ǫ) log(1 − ǫ) + ǫ − ǫ log(ǫ) = 1 − ǫ log(ǫ) − (1 − ǫ) log(1 − ǫ) 4. The mutual information is I(X; Y ) = H(X) + H(Y ) − H(X, Y ), which we can evaluate from the quantities above as: 1 + ǫ log(ǫ) + (1 − ǫ) log(1 − ǫ). 5. In the two cases of ǫ ...
... = −(1 − ǫ) log(0.5(1 − ǫ)) − ǫ log(0.5ǫ) = (1 − ǫ) − (1 − ǫ) log(1 − ǫ) + ǫ − ǫ log(ǫ) = 1 − ǫ log(ǫ) − (1 − ǫ) log(1 − ǫ) 4. The mutual information is I(X; Y ) = H(X) + H(Y ) − H(X, Y ), which we can evaluate from the quantities above as: 1 + ǫ log(ǫ) + (1 − ǫ) log(1 − ǫ). 5. In the two cases of ǫ ...
Fuzzy measure and probability distributions: distorted
... However, although Sugeno and Choquet integrals are powerful operators, their practical application is more difficult due to the fact that they require a large number of parameters. In fact, fuzzy measures require 2|X| parameters (where |X| is the number of information sources or input variables) be ...
... However, although Sugeno and Choquet integrals are powerful operators, their practical application is more difficult due to the fact that they require a large number of parameters. In fact, fuzzy measures require 2|X| parameters (where |X| is the number of information sources or input variables) be ...
(pdf)
... If X is a random variable, then for every Borel subset B of R, X −1 (B) ∈ F. We define a measure µX , called the distribution of the random variable, on Borel sets by µX (B) := P{X ∈ B} = {X −1 (B)}. If µX takes values only for countable subsets of the real numbers, X is a discrete random variable; ...
... If X is a random variable, then for every Borel subset B of R, X −1 (B) ∈ F. We define a measure µX , called the distribution of the random variable, on Borel sets by µX (B) := P{X ∈ B} = {X −1 (B)}. If µX takes values only for countable subsets of the real numbers, X is a discrete random variable; ...
Probability box
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A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes.An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shapes, including step functions, so long as they are monotonically increasing and do not cross each other. A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.