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The problem assumes we randomly sample from a standard normal for 10 times. And ask the expected number of cases that the newly sampled number is the highest. It seems the relevant question has been discussed for the uniform, and the result has something to do with $\sum_{i=1}^n1/i$.

I wonder whether the same logic applies here. For example, the probability for the second sample to be larger than the first one is $1/2$, and the probability for the third sample to be larger than the first and the second one is $1/3$. I must miss out something as the information of having a standard normal is not used. Please advise. Thanks~~

WWSS
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    You get the same result for any continuous distribution (uniform, Gaussian, and so on). The probability of any two samples being identical is zero, and out of $k$ samples, each sample is equally likely to be highest. – Michael Sep 01 '21 at 20:36
  • this is a combinatoric question: one of the samples must be the highest, but it could be in any order. – user619894 Sep 01 '21 at 20:42

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