![arXiv:math/0610716v2 [math.PR] 16 Feb 2007](http://s1.studyres.com/store/data/014486155_1-5585348474c4e163d9225232ca2e759f-300x300.png)
arXiv:math/0610716v2 [math.PR] 16 Feb 2007
... points. Ignoring probability zero events, as we may, two vertices are adjacent if and only if their cells have a common boundary arc. (Two cells may share more than one boundary arc; there is an example in Figure 1.) Our aim is to study site percolation on the random graph GP , or, equivalently, ‘f ...
... points. Ignoring probability zero events, as we may, two vertices are adjacent if and only if their cells have a common boundary arc. (Two cells may share more than one boundary arc; there is an example in Figure 1.) Our aim is to study site percolation on the random graph GP , or, equivalently, ‘f ...
Old notes from a probability course taught by Professor Lawler
... only intended to be a brief introduction — this might be considered what every graduate student should know about the theory of probability. Probability uses some different terminology than that of Lebesgue integration in R. These notes will introduce the terminology and will also relate these ideas ...
... only intended to be a brief introduction — this might be considered what every graduate student should know about the theory of probability. Probability uses some different terminology than that of Lebesgue integration in R. These notes will introduce the terminology and will also relate these ideas ...
MATH/STAT 341: PROBABILITY: FALL 2016 COMMENTS ON HW
... don’t miss anything. We start with all the ways where the first six rolled is from the first die. After we exhaust all those, we then turn to all the ways where the first six rolled is from the second die, and so on. Again letting ∗ denote a non-6, we find ...
... don’t miss anything. We start with all the ways where the first six rolled is from the first die. After we exhaust all those, we then turn to all the ways where the first six rolled is from the second die, and so on. Again letting ∗ denote a non-6, we find ...
The Enigma Of Probability - Center for Cognition and Neuroethics
... the scattered philosophical situation we have today for the probability concept. It is easy to state the St. Petersburg problem. Let us say we play a very simple game where you toss an ordinary coin until heads comes up. If heads comes up in the first toss you will get one dollar from me. If it come ...
... the scattered philosophical situation we have today for the probability concept. It is easy to state the St. Petersburg problem. Let us say we play a very simple game where you toss an ordinary coin until heads comes up. If heads comes up in the first toss you will get one dollar from me. If it come ...
Linear Hashing Is Awesome - IEEE Symposium on Foundations of
... Ωp nq and leave as an open problem to decide which nontrivial properties p q has. We make the first progress on this fundamental problem, by showing that the expected length of the longest chain is at most n1{3 op1q which means that the performance of p q is similar to that of a 3-independent ...
... Ωp nq and leave as an open problem to decide which nontrivial properties p q has. We make the first progress on this fundamental problem, by showing that the expected length of the longest chain is at most n1{3 op1q which means that the performance of p q is similar to that of a 3-independent ...
Confirmation Theory
... probability of a proposition is some person’s degree of belief in the proposition. Degree of belief is also called subjective probability, so on this view, inductive probability is the same as subjective probability. However, this is not correct. Suppose, for example, that I claim that scientific th ...
... probability of a proposition is some person’s degree of belief in the proposition. Degree of belief is also called subjective probability, so on this view, inductive probability is the same as subjective probability. However, this is not correct. Suppose, for example, that I claim that scientific th ...
Frequentism as a positivism: a three-tiered interpretation of probability
... defined by real-world frequency, then we have seemingly have no way to express the idea that an observed frequency might be aberrant, just as defining temperature to be thermometer readings leaves us with no way to express the idea that our thermometers may be inaccurate. This problem becomes especi ...
... defined by real-world frequency, then we have seemingly have no way to express the idea that an observed frequency might be aberrant, just as defining temperature to be thermometer readings leaves us with no way to express the idea that our thermometers may be inaccurate. This problem becomes especi ...
Response
... other cannot, and vice versa. We can say they are non-overlapping, the same as disjoint or mutually exclusive. For any two non-overlapping events A and B, P(A or B)=P(A) + P(B). Note 1: Events “female” and “getting an A” do overlapRule does not apply. Note 2: The word “or” entails addition. ©2011 B ...
... other cannot, and vice versa. We can say they are non-overlapping, the same as disjoint or mutually exclusive. For any two non-overlapping events A and B, P(A or B)=P(A) + P(B). Note 1: Events “female” and “getting an A” do overlapRule does not apply. Note 2: The word “or” entails addition. ©2011 B ...
Strong Normality of Numbers - CECM
... Borel’s original definition of normality [Borel 1909] had the advantage of great simplicity. None of the current profusion of concatenated monsters had been studied at the time, so there was no need for a stronger definition. However, one would like a test or a set of tests to eliminate exactly thos ...
... Borel’s original definition of normality [Borel 1909] had the advantage of great simplicity. None of the current profusion of concatenated monsters had been studied at the time, so there was no need for a stronger definition. However, one would like a test or a set of tests to eliminate exactly thos ...
Same-Decision Probability: A Confidence Measure for
... Here, we denote Pr (d | e, h) using Q(h) to emphasize our view on the probability Pr (d | e) as an expectation E[ Q(H) ] with respect to the distribution Pr (H | e) over unobserved variables H. We remark that the same-decision probability P(Q(H) ≥ T ) is also an expectation, as in Equation 2. We vie ...
... Here, we denote Pr (d | e, h) using Q(h) to emphasize our view on the probability Pr (d | e) as an expectation E[ Q(H) ] with respect to the distribution Pr (H | e) over unobserved variables H. We remark that the same-decision probability P(Q(H) ≥ T ) is also an expectation, as in Equation 2. We vie ...
Infinite monkey theorem
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.In this context, ""almost surely"" is a mathematical term with a precise meaning, and the ""monkey"" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. One of the earliest instances of the use of the ""monkey metaphor"" is that of French mathematician Émile Borel in 1913, but the first instance may be even earlier. The relevance of the theorem is questionable—the probability of a universe full of monkeys typing a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero). It should also be noted that real monkeys don't produce uniformly random output, which means that an actual monkey hitting keys for an infinite amount of time has no statistical certainty of ever producing any given text.Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. The history of these statements can be traced back to Aristotle's On Generation and Corruption and Cicero's De natura deorum (On the Nature of the Gods), through Blaise Pascal and Jonathan Swift, and finally to modern statements with their iconic simians and typewriters. In the early 20th century, Émile Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics.