![Advanced Algebra](http://s1.studyres.com/store/data/009231062_1-774d7af461be6fa26ea059c83ed3c78c-300x300.png)
Belief-type probability
... Since its 95% probable that I get a coke now, a price of $0.95 is fair: Expected value = zero. It would be unfair to be forced to use this machine even if it is “fair” in the long run. ...
... Since its 95% probable that I get a coke now, a price of $0.95 is fair: Expected value = zero. It would be unfair to be forced to use this machine even if it is “fair” in the long run. ...
File - Different Uses for Labs
... equal to 1 – p. The random variable r is used to count the number of successes out of n trials. Complete Parts I and IV using the answer key posted in Moodle. Work through parts II and III as an example of how to use the calculator to complete these exercises. I. ...
... equal to 1 – p. The random variable r is used to count the number of successes out of n trials. Complete Parts I and IV using the answer key posted in Moodle. Work through parts II and III as an example of how to use the calculator to complete these exercises. I. ...
This is just a test to see if notes will appear here…
... to spice things up. She still has 12 beads, but this time there are 5 red, 6 blue and 1 green. Crazier still, when she picks one out this time, she decides not to put it back! What is the probability that after two picks, Sarah has two beads that are the same colour? Okay, this is a bit of a tricky ...
... to spice things up. She still has 12 beads, but this time there are 5 red, 6 blue and 1 green. Crazier still, when she picks one out this time, she decides not to put it back! What is the probability that after two picks, Sarah has two beads that are the same colour? Okay, this is a bit of a tricky ...
Random Numbers
... random number table. For truly random numbers, the choice of a digit should not be affected by what is chosen previously. There are statistical tests for checking whether the lengths of run are consistent with random behavior. Warning: One shouldn’t keep using the same part of a random number table ...
... random number table. For truly random numbers, the choice of a digit should not be affected by what is chosen previously. There are statistical tests for checking whether the lengths of run are consistent with random behavior. Warning: One shouldn’t keep using the same part of a random number table ...
October 7th lecture
... one event OR another OR… is obtained by adding their individual probabilities, provided the events are ...
... one event OR another OR… is obtained by adding their individual probabilities, provided the events are ...
In Discrete Time a Local Martingale is a Martingale under an
... (wt−1 C) ∩ B0 is strongly closed in L2 (µt ). An L2 (µt )-convergent sequence in (wt−1 C) ∩ B0 is convergent in probability, so admits a subsequence convergent µt -almost surely, so P -a.s. and, by the assumption, its limit is an element of the considered set. 2 Finally, we recall the very first the ...
... (wt−1 C) ∩ B0 is strongly closed in L2 (µt ). An L2 (µt )-convergent sequence in (wt−1 C) ∩ B0 is convergent in probability, so admits a subsequence convergent µt -almost surely, so P -a.s. and, by the assumption, its limit is an element of the considered set. 2 Finally, we recall the very first the ...
Determine whether the events are independent or dependent. Then
... socks in his drawer. If he selects three socks at random with no replacement, what is the probability that he will first select a blue sock, then a black sock, and then another blue sock? SOLUTION: Since the socks are being selected with out replacement, the events are dependent. ...
... socks in his drawer. If he selects three socks at random with no replacement, what is the probability that he will first select a blue sock, then a black sock, and then another blue sock? SOLUTION: Since the socks are being selected with out replacement, the events are dependent. ...
Computation of the Probability of Initial Substring Generation by
... The purpose of this article is to develop an algorithm for computing the probability that a stochastic context-free grammar (SCFG) (that is, a grammar whose production rules have attached to them a probability of being used) generates an arbitrary initial substring of terminals. Thus, we treat the s ...
... The purpose of this article is to develop an algorithm for computing the probability that a stochastic context-free grammar (SCFG) (that is, a grammar whose production rules have attached to them a probability of being used) generates an arbitrary initial substring of terminals. Thus, we treat the s ...
Infinite monkey theorem
![](https://commons.wikimedia.org/wiki/Special:FilePath/Monkey-typing.jpg?width=300)
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.