8dataa - Logan Elm Schools
... Student's explanation shows understanding of strategy that can be used for determining number of degrees in a sector other than the 180° sector for alternative rock. Sketch may or may not be included. OR Student makes reasonable sketch and gives clear explanation based on fractional parts of circle. ...
... Student's explanation shows understanding of strategy that can be used for determining number of degrees in a sector other than the 180° sector for alternative rock. Sketch may or may not be included. OR Student makes reasonable sketch and gives clear explanation based on fractional parts of circle. ...
Math 411 Solutions to Exam 1 October 2, 2001 1. (10) A large basket
... k slots are filled with s’s and whose last (n − k) slots are filled with f’s. This represents the event that the first k tosses were heads and the last n − k tosses were tails. Since each toss is independent of the outcome of any other toss, the probability of this event is pk (1 − p). As there are ...
... k slots are filled with s’s and whose last (n − k) slots are filled with f’s. This represents the event that the first k tosses were heads and the last n − k tosses were tails. Since each toss is independent of the outcome of any other toss, the probability of this event is pk (1 − p). As there are ...
David Howie, Interpreting Probability
... For instance, more careful discussions of the work of Kolmogorov, de Finetti, and Popper would have been useful here. At one point, Howie (219) claims that Kolmogorov “defined probability as a measure property of a set within a field constructed according to a series of axioms.” Later in the chapter ...
... For instance, more careful discussions of the work of Kolmogorov, de Finetti, and Popper would have been useful here. At one point, Howie (219) claims that Kolmogorov “defined probability as a measure property of a set within a field constructed according to a series of axioms.” Later in the chapter ...
Full text
... where b is an integer _> 2. Then we may consider Am to be the base b representation of a number between 0 and 1. Then Theorem 4 implies that this number is irrational if and only if B - BR. As the last result of this paper, we state a theorem giving a description similar to that in Theorem 3 for ano ...
... where b is an integer _> 2. Then we may consider Am to be the base b representation of a number between 0 and 1. Then Theorem 4 implies that this number is irrational if and only if B - BR. As the last result of this paper, we state a theorem giving a description similar to that in Theorem 3 for ano ...
File
... and two catchers. Each outfielder can play any of the three outfield positions, and each infielder can play any of the four infield positions. In how many ways can a team of nine players be chosen? ...
... and two catchers. Each outfielder can play any of the three outfield positions, and each infielder can play any of the four infield positions. In how many ways can a team of nine players be chosen? ...
Paradoxes in Probability Theory, by William
... to one-box is a no-brainer. But why should I accept that those conditional probabilities apply to me, just because they arise as observed frequencies in a large population of other people? It seems that most people would resist such a conclusion, and that there are (at least) two psychological reaso ...
... to one-box is a no-brainer. But why should I accept that those conditional probabilities apply to me, just because they arise as observed frequencies in a large population of other people? It seems that most people would resist such a conclusion, and that there are (at least) two psychological reaso ...
Uniform Laws of Large Numbers
... The bounds above obtained from Tchebychev’s inequality are very poor. By using Chernoff’s method an exponential bound can be obtained. In fact we have, Hoeffding’s inequality ...
... The bounds above obtained from Tchebychev’s inequality are very poor. By using Chernoff’s method an exponential bound can be obtained. In fact we have, Hoeffding’s inequality ...
Random Variables Generation
... For simulation, the random numbers generator must have the following desire properties: 1. It should produce numbers that are random. 2. It should be fast. 3. It should not require much computer storage. 4. It should have a long period before cycling. The object is to select a generation method that ...
... For simulation, the random numbers generator must have the following desire properties: 1. It should produce numbers that are random. 2. It should be fast. 3. It should not require much computer storage. 4. It should have a long period before cycling. The object is to select a generation method that ...
Paradoxes in Probability Theory
... to one-box is a no-brainer. But why should I accept that those conditional probabilities apply to me just because they arise as observed frequencies in a large population of other people? It seems that most people would resist such a conclusion and that there are (at least) two psychological reasons ...
... to one-box is a no-brainer. But why should I accept that those conditional probabilities apply to me just because they arise as observed frequencies in a large population of other people? It seems that most people would resist such a conclusion and that there are (at least) two psychological reasons ...
Lectures Notes (Motifs discovery).
... Assuming that the motifs are equally likely to occur at any position in the sequences, specifying Pr(i) is straightforward, and so is computing Pr(D | w). Optimizing it with respect to w, however, is not, and numerical optimization is necessary. One such approach is the expectation-maximization (EM) ...
... Assuming that the motifs are equally likely to occur at any position in the sequences, specifying Pr(i) is straightforward, and so is computing Pr(D | w). Optimizing it with respect to w, however, is not, and numerical optimization is necessary. One such approach is the expectation-maximization (EM) ...
Math 55, Probability Worksheet #2 March 19, 2014 1. What is the
... 4. Consider a family with n children. Let E be the event that the family has at least one child of each gender and let F be the event that the family as at most one boy. For which n (if any) are E and F independent? Assume that birth order matters, so the sets {boy, girl} and {girl, boy} are differe ...
... 4. Consider a family with n children. Let E be the event that the family has at least one child of each gender and let F be the event that the family as at most one boy. For which n (if any) are E and F independent? Assume that birth order matters, so the sets {boy, girl} and {girl, boy} are differe ...
Csorgo, Sandor and Simon, Gordon; (1994).A Strong Law of Large Numbers for Trimmed Sums, with Applications to Generalized St. Petersburg Games."
... The prototypical example, when light trimming is definitely needed for a strong law, is provided by the classical St. Petersburg game, a generalized version of which is discussed in Section 3. Feller (1945, cf. also Section XA of 1968a) used this game to illustrate a weak law in the spirit of (1.12) ...
... The prototypical example, when light trimming is definitely needed for a strong law, is provided by the classical St. Petersburg game, a generalized version of which is discussed in Section 3. Feller (1945, cf. also Section XA of 1968a) used this game to illustrate a weak law in the spirit of (1.12) ...
Richard D. Gill
... For a mathematician it helps to introduce some more notation. I’ll refer to the envelopes as A and B, and the amounts in them as A and B. Let me introduce X to stand for the smaller of the two amounts and Y to stand for the larger. I think of all four as being random variables; but this includes th ...
... For a mathematician it helps to introduce some more notation. I’ll refer to the envelopes as A and B, and the amounts in them as A and B. Let me introduce X to stand for the smaller of the two amounts and Y to stand for the larger. I think of all four as being random variables; but this includes th ...
Probability - ANU School of Philosophy
... relative frequencies in suitable infinite sequences of trials. If there are in fact only finitely many trials of the relevant type, then this requires the actual sequence to be extended to a hypothetical or ‘virtual’ sequence. This creates new difficulties. For instance, there is apparently no fact ...
... relative frequencies in suitable infinite sequences of trials. If there are in fact only finitely many trials of the relevant type, then this requires the actual sequence to be extended to a hypothetical or ‘virtual’ sequence. This creates new difficulties. For instance, there is apparently no fact ...
Counting strategies - UCLA Department of Mathematics
... 15. Six ants simultaneously stand on the six vertices of a regular octahedron, with each ant at a different vertex. Simultaneously and independently, each ant moves from its vertex to one of the four adjacent vertices, each with equal probability. What is the probability that no two ants arrive at t ...
... 15. Six ants simultaneously stand on the six vertices of a regular octahedron, with each ant at a different vertex. Simultaneously and independently, each ant moves from its vertex to one of the four adjacent vertices, each with equal probability. What is the probability that no two ants arrive at t ...
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.