answers to HW 8
... sets (1/4, 3/8) and (5/8, 3/4). In other word, you remove two open intervals 1/8 of a unit long leaving three closed intervals 1/4 of a unit long. Repeat the process infinitely often. Each time you remove two open pieces from each interval that you have leaving three closed intervals which are exact ...
... sets (1/4, 3/8) and (5/8, 3/4). In other word, you remove two open intervals 1/8 of a unit long leaving three closed intervals 1/4 of a unit long. Repeat the process infinitely often. Each time you remove two open pieces from each interval that you have leaving three closed intervals which are exact ...
p(x)
... Since continuous probability functions are defined for an infinite number of points over a continuous interval, the area under the curve between two distinct points defines the probability for that interval. (Probabilities are measured over intervals, not single points. The probability at a single p ...
... Since continuous probability functions are defined for an infinite number of points over a continuous interval, the area under the curve between two distinct points defines the probability for that interval. (Probabilities are measured over intervals, not single points. The probability at a single p ...
Introduction Introduction to probability theory
... Combinatorial results then helps us to derive the following probabilities for X. ...
... Combinatorial results then helps us to derive the following probabilities for X. ...
Arches and Loops and Whorls, Oh My! A Study of Fingerprint Patterns
... Based on the 200 million fingerprint files the FBI has, using a proportionate equation, I calculated about how many people have certain types of prints. However, I will have to perform the experiment on a much larger scale to get a truer picture, because according to the Ventura County Crimb Lab, fr ...
... Based on the 200 million fingerprint files the FBI has, using a proportionate equation, I calculated about how many people have certain types of prints. However, I will have to perform the experiment on a much larger scale to get a truer picture, because according to the Ventura County Crimb Lab, fr ...
Independent and Dependent Events Notes
... Example: Suppose you spin each of these two spinners. What is the probability of spinning an even number and a vowel? ...
... Example: Suppose you spin each of these two spinners. What is the probability of spinning an even number and a vowel? ...
Sigmund Freud was born in the year:
... 585 square km. b) 226 square km. Probability____________ ...
... 585 square km. b) 226 square km. Probability____________ ...
unit 3 module 4
... Note that the classical definition of probability does not apply in this case, because we can't break this experiment down into a set of equally likely outcomes. For instance, one outcome of the experiment is the situation where no bottles are toppled. Another outcome is the case where 1 bottle is t ...
... Note that the classical definition of probability does not apply in this case, because we can't break this experiment down into a set of equally likely outcomes. For instance, one outcome of the experiment is the situation where no bottles are toppled. Another outcome is the case where 1 bottle is t ...
Stat 421 Solutions for Homework Set 1 Page 15 Exercise 1
... Since this conclusion contradicts the initial supposition, m m n j=m j j=m j it must be true that x does belong to infinitely many of A1 , A2 , . . . ,. ’⇐’ Now we assume that x is in infinitely many Ai . Then, for every n, there is a value of j > n such that ...
... Since this conclusion contradicts the initial supposition, m m n j=m j j=m j it must be true that x does belong to infinitely many of A1 , A2 , . . . ,. ’⇐’ Now we assume that x is in infinitely many Ai . Then, for every n, there is a value of j > n such that ...
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.