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# Category Archives: Probability

## Generating a random variable by coin tossing

1. Coin tossing Suppose we are given a sequence of independent fair bits (meaning take and with probabily ) we want to produce with them a discrete random variable that takes the values with probabilities . The objective, of course, … Continue reading

Posted in Algorithms, Number Theory, Probability
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## Grading a class

Imagine we had a class with students and each week they hand in a sheet of homework. Now, you choose a set of of them at random and correct only those . At the end, the grade assigned to a … Continue reading

Posted in Asymptotics, Combinatorics, Computation, Probability
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## Generating a random permutation

It is well-known that any permutation of can be written as a product of transpositions, that is, of permutations of the form with , where we recall that is the permutation satisfying and for . In this post however, we … Continue reading

Posted in Combinatorics, Computation, Probability
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## Symmetric random walks

Definition 1 A symmetric random walk is a homogeneous Markov chain on the set of states such that with probability , and for all . In plain terms, this means that we start off at , and at each second … Continue reading

## More on the Monkey typing problem

To compute the expected number of letters the monkey must type before our word turns up, we used . It is clear that when the series on the left hand side converges, that is the result of the series, … Continue reading

Posted in Graph Theory, Linear Algebra, Probability
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## Monkey typing!

I find this an amusing idea, you have a monkey typing on a keyboard and what we want to know is roughly how long we will have to wait for a certain word – a name for instance- to be … Continue reading

Posted in Probability
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