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Uniform Distribution of Sequences Modulo $2\pi$

It's more traditional to study equidistribution mod $1$ rather than $2\pi$, but of course they are related: $a_n \mod 1 = (2 \pi a_n \mod 2\pi)/(2\pi)$.See Equidistributed sequence. Equidistribution ...
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Accepted

The discrete PDF $p_\alpha(k) = |\binom{\alpha}{k}|$, $\alpha \in (0,1)$

It is called the Sibuya distribution with generating function $1-(1-z)^{\alpha}.$ Just google for numerous references.
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Strange consequence of linear combination of normal distribution

You have added "independent" to your claim. But then the $Y+Y$ in your question is confusing. If $Y_1 \sim N(0,1)$ and independently $Y_2 \sim N(0,1)$ then $U=Y_1+Y_1=2Y_1 \sim N(0,4)$ ...
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Accepted

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1 vote

Robot Capture the flag

I think the initial strategy from the other solution is correct, but it's possible to update Aaron's strategy to improve his probability of winning somewhat. I'm not completely sure that my ...
1 vote

Robot Capture the flag

I feel like I may have misunderstood the question so please tell me if I have done so. Firstly, it is reasonable to find what the optimal strategies actually are for Erin and Aaron. Since Erin knows ...
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