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中文题目Exchange a ticks and Exchange B ticks arrive as independent Poisson processes with rates $\lambda_A=9$ and $\lambda_B=3$ per hour. What is the probability that the next arrival in the merged stream comes from stream A?
打开 →The map $x=u+v,\ y=u-v$ sends the unit square $0\le u,v\le 1$ to a parallelogram. What is its area?
打开 →The map $x=2u,\ y=3v$ sends the unit disk $u^2+v^2\le 1$ to an ellipse in the $(x,y)$-plane. What is the area of that ellipse?
打开 →The map $x=u,\ y=u+2v$ sends the unit square to a parallelogram. Compute the image area.
打开 →Two independent exchanges send quotes to your gateway. Exchange A is a Poisson process with rate 3 per minute and exchange B is an independent Poisson process with rate 5 per minute. Treating the combined stream as one process, what is the probability that no quote arrives during
打开 →A sultan offers a vizier the hand of one of 5 daughters, presented one at a time in uniformly random order. After meeting a daughter, the vizier learns only how she ranks (by dowry) relative to those already seen and must immediately and irrevocably accept or send her away; if he
打开 →A primary split is missing for some rows, so a surrogate split is trained on the M rows where the primary feature is observed. If it sends A of those rows to the same side as the primary split, what is its agreement rate?
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