There are two types of incoming calls to a telephone office. The first type requires commercial information and the second type not. Suppose the arrival of these two types of calls can be represented by separate Poisson processes with rates $\lambda_{1}$ and $\lambda_{2}$. What is the probability that between two non-business calls come five business calls?
2026-04-02 06:06:49.1775110009
Independent Poisson process properties
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Hint: each call is of type $1$ with probability $p = \lambda_1/(\lambda_1 + \lambda_2)$ and type $2$ with probability $q = 1-p$, and different calls are independent. Geometric distribution...