![5-83. Darnell designed the spinner at right for a game. It still has one](http://s1.studyres.com/store/data/019721432_1-3e01f834e5e0974456d546aaaefa15e2-300x300.png)
Random Number Generator
... represent random events Supporting randomness contributes to the evaluation of systems in different possible states Computers by nature are not random (they do as they programmed to) Therefore Random Number Generators are ...
... represent random events Supporting randomness contributes to the evaluation of systems in different possible states Computers by nature are not random (they do as they programmed to) Therefore Random Number Generators are ...
Study Materials
... Note: An event having only one outcome of the experiment is called an elementary event. In the above example P(Y)+P(R)+P(B)=1 Observe that the sum of the probabilities of all the elementary events of an experiment is1.This is true in general also. Example 3 Suppose we throw a true die once(I)What is ...
... Note: An event having only one outcome of the experiment is called an elementary event. In the above example P(Y)+P(R)+P(B)=1 Observe that the sum of the probabilities of all the elementary events of an experiment is1.This is true in general also. Example 3 Suppose we throw a true die once(I)What is ...
Notes: Independent and Dependent Probability 1. If an 8
... Notes: Independent and Dependent Probability 1. If an 8-sided die is rolled once, what is the probability of rolling an even number and a number less than five? Independent/ Dependent ...
... Notes: Independent and Dependent Probability 1. If an 8-sided die is rolled once, what is the probability of rolling an even number and a number less than five? Independent/ Dependent ...
CHAPTER 5. Convergence of Random Variables
... One of the most important parts of probability theory concerns the behavior of sequences of random variables. This part of probability is often called “large sample theory” or “limit theory” or “asymptotic theory.” This material is extremely important for statistical inference. The basic question is ...
... One of the most important parts of probability theory concerns the behavior of sequences of random variables. This part of probability is often called “large sample theory” or “limit theory” or “asymptotic theory.” This material is extremely important for statistical inference. The basic question is ...
Probability Statistics Student Module
... of five different contests going on right now, but only has three postage stamps. In how many ways can she select three of the five contests to enter? ...
... of five different contests going on right now, but only has three postage stamps. In how many ways can she select three of the five contests to enter? ...
Exact upper tail probabilities of random series
... j=1 aj ξj with i.i.d. random variables {ξj } which are not heavytailed. More precisely, the distribution of ξj is assumed to have an exponential tail with rate γ ≥ 0 (cf. [3] and [5]): ...
... j=1 aj ξj with i.i.d. random variables {ξj } which are not heavytailed. More precisely, the distribution of ξj is assumed to have an exponential tail with rate γ ≥ 0 (cf. [3] and [5]): ...
Sample Distributions
... ____ 49. A Bernoulli trial has a probability of success of 0.4. What is the smallest number of trials for which a normal distribution can be used to approximate its probability distribution? a. 12.5 c. 10 b. 20 d. 13 ____ 50. The z-score for a particular value of X is 0.18. What is the total probabi ...
... ____ 49. A Bernoulli trial has a probability of success of 0.4. What is the smallest number of trials for which a normal distribution can be used to approximate its probability distribution? a. 12.5 c. 10 b. 20 d. 13 ____ 50. The z-score for a particular value of X is 0.18. What is the total probabi ...
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.