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Questions tagged [probability]

For basic questions about probability and for questions about calculating a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using [tag:measure theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

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If $X\sim \mathrm{lognormal}$ then $Y:=(X-d|x\geq d)$ has approximately a Generalized Pareto distribution.

Let $X$ be a random variable with lognormal distribution. Show that when sufficiently large then $Y:=(X-d|x\geq d)$ is approximately a random variable with generalized Pareto distribution. Hint: Use ...
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2answers
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If $S_n$ is Binomial $(n,p)$ then $\mathbb P(S_n=k)\approx \frac{(np)^k}{k!}e^{-np}$.

I was reading this post, and I have to admit that I was quite confused. The question was : If $S_n$ is a Binomial r.v. with parameter $(n,p)$ s.t. $n$ large, $p$ very small and $np$ not to big (for ...
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+100

What mean : $R^x$ is the probability that $Y_t$ start at $x$?

Here the context : I'm a bit confuse by the notation, since he defines $Y_t=Y_t^x$, and at the bottom, he says that $R^x$ is the probability that $Y_t$ start at $x$, and after he writes $$R^x(Y_{t_1}\...