Constructing k-wise Independent Variables
... Induction step: We will show the statement still holds when |T | = s + 1 ≤ k. Since G is k-unique and |T | ≤ k, there is an element of T , call it x0 , that has a neighbor r0 that none of the other elements of T have as a neighbor. By the induction hypothesis, T \ {x0 } are linearly independent, and ...
... Induction step: We will show the statement still holds when |T | = s + 1 ≤ k. Since G is k-unique and |T | ≤ k, there is an element of T , call it x0 , that has a neighbor r0 that none of the other elements of T have as a neighbor. By the induction hypothesis, T \ {x0 } are linearly independent, and ...
Confidence Intervals
... Many types of confidence intervals exist for various kinds of parameters. Ch. 14: Confidence Intervals for mean (s.d. σ is known). Ch. 18: Confidence Intervals for mean (s.d. σ is unknown). Ch. 19: Confidence Intervals for difference between two population means. Ch. 20: Confidence Intervals for ...
... Many types of confidence intervals exist for various kinds of parameters. Ch. 14: Confidence Intervals for mean (s.d. σ is known). Ch. 18: Confidence Intervals for mean (s.d. σ is unknown). Ch. 19: Confidence Intervals for difference between two population means. Ch. 20: Confidence Intervals for ...
ap statistics
... Safety officials hope a public information campaign will increase the use of seatbelts above the current 70% level. Their efforts include running radio and TV ads, putting up billboards, having police officers appear on talk shows, and getting newspapers to indicate whether people injured in acciden ...
... Safety officials hope a public information campaign will increase the use of seatbelts above the current 70% level. Their efforts include running radio and TV ads, putting up billboards, having police officers appear on talk shows, and getting newspapers to indicate whether people injured in acciden ...
here
... S = {HH, HT, TH, TT}. Our sample space consists of 4 points, each of which is equally likely to occur. P(HH) = 1/4. Let E= at least one head = {HH, HT, TH}. P(E) = ¾. Let F= exactly one head = {HT, TH}. P(E) = 2/4 = 1/2. Ex. Roll two dice. S={(i,j) | i=1,….6, j=1,….6 } There are 36 possible outcomes ...
... S = {HH, HT, TH, TT}. Our sample space consists of 4 points, each of which is equally likely to occur. P(HH) = 1/4. Let E= at least one head = {HH, HT, TH}. P(E) = ¾. Let F= exactly one head = {HT, TH}. P(E) = 2/4 = 1/2. Ex. Roll two dice. S={(i,j) | i=1,….6, j=1,….6 } There are 36 possible outcomes ...
Probability - ANU School of Philosophy
... belief’. Underpinning subjectivism are so-called ‘Dutch Book arguments’. They begin by identifying agents’ degrees of belief with their betting dispositions, and they then show that anyone whose degrees of belief violate the axioms of probability is ‘incoherent’— susceptible to guaranteed losses at ...
... belief’. Underpinning subjectivism are so-called ‘Dutch Book arguments’. They begin by identifying agents’ degrees of belief with their betting dispositions, and they then show that anyone whose degrees of belief violate the axioms of probability is ‘incoherent’— susceptible to guaranteed losses at ...
Probability of Events
... The card that is dealt first has no influence on which card is dealt second, third, or fourth (because the card is replaced before the next draw) The card that is dealt second has no influence on which card is dealt first, third, or fourth, and so on Thus the draws are independent events ...
... The card that is dealt first has no influence on which card is dealt second, third, or fourth (because the card is replaced before the next draw) The card that is dealt second has no influence on which card is dealt first, third, or fourth, and so on Thus the draws are independent events ...
U.C. Berkeley — CS270: Algorithms Lectures 13, 14 Scribe: Anupam
... Consider the following simpler version of approximate counting: The output should be ‘yes’ if the number of distinct items N is more than 2k, ‘no’ if N is less than k and we do not care about the output if k ≤ N ≤ 2k. ...
... Consider the following simpler version of approximate counting: The output should be ‘yes’ if the number of distinct items N is more than 2k, ‘no’ if N is less than k and we do not care about the output if k ≤ N ≤ 2k. ...
Thermodynamics of natural images
... clear peak as a function of temperature, and this peak is shifting toward T = 1. To calibrate our intuition about the specific heat estimated from small patches, we have done precisely analogous computations on the nearest neighbor ferromagnetic Ising P model in two Pdimensions, defined by E(~σ ) = ...
... clear peak as a function of temperature, and this peak is shifting toward T = 1. To calibrate our intuition about the specific heat estimated from small patches, we have done precisely analogous computations on the nearest neighbor ferromagnetic Ising P model in two Pdimensions, defined by E(~σ ) = ...
ppt - College of Computer and Information Science
... A random variable (RV) is a variable characterized by random behavior in assuming its different possible values. A stochastic model (or theory) is a set of RVs. The model is completely specified by the joint probability distribution (JPD) of the RVs. As the number of RVs increases, the compl ...
... A random variable (RV) is a variable characterized by random behavior in assuming its different possible values. A stochastic model (or theory) is a set of RVs. The model is completely specified by the joint probability distribution (JPD) of the RVs. As the number of RVs increases, the compl ...
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.