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Expected number of steps until a queue of $n$ people has passed all $n$ ordered tests consecutively

We are given a queue of $n$ people $\{p_1, \ldots, p_n\}$. They each have to pass $n$ exams $\{t_1, \ldots, t_n\}$. For simplicity we can "draw" the setting in the following way: $$[t_n,t_{n-...
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If $\text P\left[X_2\in B_2\mid X_1\right]=\kappa(X_1,B_2)$ a.s. for all $B_2$, can we select a common null-set over all $B_2$?

Let $(\Omega,\mathcal A,\operatorname P)$ be a probability space $(E_i,\mathcal E_i)$ be a measurable space $X_1:\Omega\to E_1$ $X_2:\Omega\to E_2$ be $(\mathcal A,\mathcal E_2)$-measurable $\kappa$ ...
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A closed form of mean-field equations

Assume that a system at time t, for example number of costumers in a line at time $t$ which is denoted by $q(t)$, follows a Markov chain with these dynamics (probabilities) $$P(q(t+\Delta t)-q(t)=1)=\...
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