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6004概率中等数值题medium

Short-Window Linear Approximation Error

题目

Spikes arrive at a detector as a Poisson process with rate 3 per minute. For a very short 0.5-second window the probability of at least one spike is often approximated by λt\lambda t. What is the absolute error of that approximation, i.e. λtP(N1)\lambda t - P(N\ge 1)? Give a decimal to four places.

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