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Results tagged with pr.probability
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user 65801
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
15
votes
Throwing a fair die until most recent roll is smaller than previous one
The answer may be expressed more simply, in fact $E_n = \left( \frac{n}{n-1}\right)^n$.
Update 1: (The following was independently obtained by Pierre PC, I just found out after I finished typing.) The …
- 1,907
11
votes
Accepted
Show a sequence of sums involving Catalan Numbers converges
By 'magic' and a computer (see the book "A=B" by Petkovsek, Wilf and Zeilberger https://www.math.upenn.edu/~wilf/AeqB.html) the numbers $\mathcal{E}_s$ satisfies the recurrence
$\sum_{k=0}^3 P_k(s) \m …
- 1,907
3
votes
Accepted
Probability that k randomly drawn permutations can be arranged to compose to the identity
Only a partial answer, which however is too long for a comment: Let $p_{n,k}$ denote the given probability. Then we have
(1) $p_{n,1} = p_{n,2} = \frac{1}{n!}$, $p_{n,3} = \frac{2\cdot n!-p(n)}{(n!)^2 …
- 1,907