lectures 1-4
... • Theoretical (e.g. spectral test), but mostly address whole period, not guaranteed to be meaningful for shorter streams. • Empirical tests, claim to look for various aspects of (non)randomness of a given stream. Consist of computing a certain number using the given stream, comparing with result of ...
... • Theoretical (e.g. spectral test), but mostly address whole period, not guaranteed to be meaningful for shorter streams. • Empirical tests, claim to look for various aspects of (non)randomness of a given stream. Consist of computing a certain number using the given stream, comparing with result of ...
A Philosopher`s Guide to Probability
... was when he wrote it in 1736. It is almost platitudinous to point out the importance of probability in statistics, physics, biology, chemistry, computer science, medicine, law, meteorology, psychology, economics, and so on. Probability is crucial to any discipline that deals with indeterministic pro ...
... was when he wrote it in 1736. It is almost platitudinous to point out the importance of probability in statistics, physics, biology, chemistry, computer science, medicine, law, meteorology, psychology, economics, and so on. Probability is crucial to any discipline that deals with indeterministic pro ...
7th Grade Advanced Topic IV Probability, MA.7.P.7.1, MA.7.P.7.2
... She reached into the container, pulled out one shape at random, recorded its number, and put the shape back into the container. Martha did this 10 times with the results shown below. ...
... She reached into the container, pulled out one shape at random, recorded its number, and put the shape back into the container. Martha did this 10 times with the results shown below. ...
Calculator Version
... the rest of the course, you must conquer this topic Normal distributions are common There are methods to use normal distributions even if you data does not follow a normal distribution ...
... the rest of the course, you must conquer this topic Normal distributions are common There are methods to use normal distributions even if you data does not follow a normal distribution ...
Sample E with solutions
... ANSWER: Draw a picture. The region with neither coordinate between 1/3 and 2/3 consists of four squares of side length 1/3. Hence the probability that neither coordinate lies between 1/3 and 2/3 is 4/9. So the probabiity that at least one coordinate lies between 1/3 and 2/3 is 5/9. (4) You have seve ...
... ANSWER: Draw a picture. The region with neither coordinate between 1/3 and 2/3 consists of four squares of side length 1/3. Hence the probability that neither coordinate lies between 1/3 and 2/3 is 4/9. So the probabiity that at least one coordinate lies between 1/3 and 2/3 is 5/9. (4) You have seve ...
How to Use the Lafayette ESS Report to Obtain a Bayesian
... results are reported categorically as to whether the numerical test score differs at a statistically significant level from the empirical reference distributions for deception and truth-telling. Similar to the logic of hypothesis testing, the traditional statistic of interest is the p-value. The log ...
... results are reported categorically as to whether the numerical test score differs at a statistically significant level from the empirical reference distributions for deception and truth-telling. Similar to the logic of hypothesis testing, the traditional statistic of interest is the p-value. The log ...
6. Cardinality And The Strange Nature Of Infinity
... Solution: We visualize ] and ` as shown below. The arrows are inserted to help us construct a one-to-one function from ` to ] . ...
... Solution: We visualize ] and ` as shown below. The arrows are inserted to help us construct a one-to-one function from ` to ] . ...
Slides
... are set by T’s hash string are also set in the document’s signature. • Fact 2. However, a document’s signature that has all these bits set doesn’t necessarily mean that T appears in that document. Why? - Because the particular “1”-bits can be set by some other terms. ...
... are set by T’s hash string are also set in the document’s signature. • Fact 2. However, a document’s signature that has all these bits set doesn’t necessarily mean that T appears in that document. Why? - Because the particular “1”-bits can be set by some other terms. ...
Uniqueness of maximal entropy measure on essential
... simple counterexample when G is infinite, first recall that the number of topological ends of an infinite tree T is the maximum number of disjoint semi-infinite paths in T (which may be ∞). A k-ended tree is a tree with k topological ends. If G = Zd with d > 4, then µG ∈ EG and µG -almost surely F c ...
... simple counterexample when G is infinite, first recall that the number of topological ends of an infinite tree T is the maximum number of disjoint semi-infinite paths in T (which may be ∞). A k-ended tree is a tree with k topological ends. If G = Zd with d > 4, then µG ∈ EG and µG -almost surely F c ...
Document
... in continuous use, or two channels being at fifty percent use each, and so on. For example, if an office had two telephone operators who are both busy all the time, that would represent two erlangs (2 E) of traffic, or a radio channel that is occupied for thirty minutes during an hour is said to car ...
... in continuous use, or two channels being at fifty percent use each, and so on. For example, if an office had two telephone operators who are both busy all the time, that would represent two erlangs (2 E) of traffic, or a radio channel that is occupied for thirty minutes during an hour is said to car ...
lect1fin
... Is Union of denumerably infinite collection of pairwise disjoint events Ai an event? ...
... Is Union of denumerably infinite collection of pairwise disjoint events Ai an event? ...
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.