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Questions tagged [probability]

This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under (probability-theory) instead. For questions about specific probability distributions, please use (probability-distributions).

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Show that $a_{n}M_{n} - a_{n}^{2}\xrightarrow{d} Q$

Let $(X_{i})_{i}$ be IID standard normal random variables. Define $M_{n}:=\max{(X_{1},...,X_{n})}$ and $a_{n}=\sqrt{2\log(n)-\log(\log{(n)})-\log{(4\pi)}}$ Show that $a_{n}M_{n} - a_{n}^{2}\...