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Results tagged with pr.probability
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user 4213
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
Random walk on a two-dimensional uniform grid
The probability that the walk meets the diagonal at $(k,k)$ where $0 < k < n$ is
$${2k \choose k}p^k(1-p)^k$$
so the expected number of such meetings is
$$\sum_{k=1}^{n-1}{2k \choose k}p^k(1-p)^k$$
wh …
- 20.8k
12
votes
Accepted
Any sum of 2 dice with equal probability
You can write this as a single polynomial equation
$$p(x)q(x)=\frac1{11}(x^2+x^3+\cdots+x^{12})$$
where $p(x)=p_1x+p_2x^2+\cdots+p_6x^6$ and similarly for $q(x)$.
So this reduces to the question of fa …
- 20.8k
14
votes
connection between the Gaussian and the Cauchy distribution
The bivariate distribution formed by two independent
normalized Gaussians is rotationally symmetric (think about the
usual argument for evaluating the probability integral). The
quotient of two random …
- 20.8k
3
votes
An Integral and derived double integral
This can be rephrased as follows.
Let $X$ and $Y$ be independent
random variables with the same, continuous, distribution.
Is it true that $E(X)\le E(|X-Y|)$.
Is this likely?
Is it true for …