# Tagged Questions

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### Relations between stochastic Big O-Notation, limsup and lim?

I have to solve a list of exercises on probability theory but I'm having several problems in understanding the following questions; could you help me? Thank you! Let $||.||$ indicate the Euclidean ...
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### Asymptotic probability of difference of two positive random variables

Assume I have two positive, iid random variables, $X$ and $Y$. I need to compute $P\{X-Y > u\}$. I was thinking of doing $P\{X > Y + u \} = P\{X > v\}$, where $v = Y+u$. (Reason: Since $Y$ ...
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### Asymptotics of the classical occupancy problem

Classical Occupancy Problem. There are $n$ distinct labeled balls in an urn. $k$ of them of uniformly selected with replacement. What is the probability that the sample contains at least one ball ...
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### An extrasensory perception strategy :-)

Inspired by classical Joseph Banks Rhine experiments demonstrating an extrasensory perception (see, for instance, the beginning of the respective chapter of Jeffrey Mishlove book “The Roots of ...
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### How many edges does an Erdős-Rényi graph have to have, to almost surely have a component with multiple cycles?

An Erdős-Rényi graph is a random graph, selected according to the distribution obtained one where we have some number $n$ of nodes, and some probability $p$ of each potential edge being ...
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### On convergence in distribution

Let $\delta$ and $\theta$ be two estimators of the scaler parameters $\delta_0$ and $\theta_0$, respectively. Suppose that conditions are satisfied such that as the sample size $n \to \infty$, then ...
$N$ points are selected in a uniformly distributed random way in a disk of the unit radius. Let $P(N)$ and $A(N)$ denote the expected perimeter and the expected area of their convex hull. For what ...