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Infinite Monkey Theorem
... The notion that monkeys typing at random will eventually produce literature is often attributed to Thomas Huxley, a 19th-century scientist who supported Charles Darwin's theories of evolution. Mathematicians have also used it to illustrate concepts of chance. The Plymouth experiment was funded by En ...
... The notion that monkeys typing at random will eventually produce literature is often attributed to Thomas Huxley, a 19th-century scientist who supported Charles Darwin's theories of evolution. Mathematicians have also used it to illustrate concepts of chance. The Plymouth experiment was funded by En ...
Lecture-2
... A sample space is discrete if it consists of a finitely many or a countable infinite set of outcomes. In the coin-tossing example, the sample space has two outcomes and it is referred to as a finite sample space. If the elements/points of a sample space constitute a continuum - for example, all th ...
... A sample space is discrete if it consists of a finitely many or a countable infinite set of outcomes. In the coin-tossing example, the sample space has two outcomes and it is referred to as a finite sample space. If the elements/points of a sample space constitute a continuum - for example, all th ...
ST_PP_16_RandomVariables
... • Random variables that can take on any value in a range of values are called continuous random variables. • Now, any single value won’t have a probability, but… • Continuous random variables have means (expected values) and variances. • We won’t worry about how to calculate these means and varianc ...
... • Random variables that can take on any value in a range of values are called continuous random variables. • Now, any single value won’t have a probability, but… • Continuous random variables have means (expected values) and variances. • We won’t worry about how to calculate these means and varianc ...
Fractured Spaghetti and Other Probability Topics
... Part 1 was actually an attempt to approximate the probability of forming a triangle by randomly breaking spaghetti. We got only ten measurements per person. If we use computer or calculator simulation, we can easily increase the number of trials of this experiment without wasting spaghetti. Each gro ...
... Part 1 was actually an attempt to approximate the probability of forming a triangle by randomly breaking spaghetti. We got only ten measurements per person. If we use computer or calculator simulation, we can easily increase the number of trials of this experiment without wasting spaghetti. Each gro ...
Constructing k-wise Independent Variables
... which x0 does depend on. Thus, T is linearly independent. So we have shown that if we have a G that is k-unique, we have n k-wise independent variables. Which G’s are k-unique? It turns out that a random G is unique with high probability, so long as m is large enough. Our random process goes as foll ...
... which x0 does depend on. Thus, T is linearly independent. So we have shown that if we have a G that is k-unique, we have n k-wise independent variables. Which G’s are k-unique? It turns out that a random G is unique with high probability, so long as m is large enough. Our random process goes as foll ...
Randomness
![](https://en.wikipedia.org/wiki/Special:FilePath/RandomBitmap.png?width=300)
Randomness is the lack of pattern or predictability in events. A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events (or ""trials"") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will occur twice as often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than haphazardness, and applies to concepts of chance, probability, and information entropy.The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness.Randomness is most often used in statistics to signify well-defined statistical properties. Monte Carlo methods, which rely on random input (such as from random number generators or pseudorandom number generators), are important techniques in science, as, for instance, in computational science. By analogy, quasi-Monte Carlo methods use quasirandom number generators.Random selection is a method of selecting items (often called units) from a population where the probability of choosing a specific item is the proportion of those items in the population. For example, with a bowl containing just 10 red marbles and 90 blue marbles, a random selection mechanism would choose a red marble with probability 1/10. Note that a random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue. In situations where a population consists of items that are distinguishable, a random selection mechanism requires equal probabilities for any item to be chosen. That is, if the selection process is such that each member of a population, of say research subjects, has the same probability of being chosen then we can say the selection process is random.