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5997概率中等数值题medium

Expected Count Under an Unknown Regime

题目

On any given day the market is in a 'calm' regime with probability 0.5, where news events arrive as a Poisson process with rate 6 per hour, or a 'busy' regime with probability 0.5, with rate 14 per hour. Before observing the day you do not know the regime. What is the expected number of news events in a 1-hour window?

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