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Results tagged with pr.probability
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user 34435
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
1
vote
Accepted
Computation of the mean of a random variable to estimate algorithm complexity
It seems to me that $P(d>k)=\tfrac1{k+1}$ for $k\in[0,n]$, so that $$E[d]=\sum_{k\ge 0}P(d>k)=H_{n+1}\simeq \ln n.$$ The reason is that the last $k+1$ terms of the sequence are in random order, so tha …
- 456
9
votes
The probability for a streak when tossing a coin
The survey: ENUMERATION OF STRINGS by A. M. Odlyzko, available at
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.76.5995&rep=rep1&type=pdf
gives an answer for a fair coin, I think, for it …
- 456
1
vote
Maximum of a sequence of $n$ positive random variables where variance is an increasing funct...
From considerations above, I would guess that, when $n=o(\sigma(n))$, $T^{\star}(n)=\mu+\tfrac{\sigma(n)}{\mu}$ satisfies $$\lim_n\mathbb{P}(X_{max}\ge T^{\star}(n))=1,$$
for any array $X^n_i$ meeting …
- 456
5
votes
Accepted
Analogy between Integers and Permutations
The essential common feature that insures convergence to a Poisson Dirichlet distribution is explained in the book "Logarithmic Combinatorial Structures" by Arratia Barbour and Tavare. They do a great …
- 456
1
vote
Analogy between Integers and Permutations
If I remember well, there is also a correspondence between the degrees of factors of polynomials in $\mathbb{F}_q[X]$, the size of cycles of riffle-shuffle permutations (a brand of non-uniform random …
- 456