The process by which certain pulses are emitted in a human body is modeled as a Poisson process. In other words, the times 𝑌 𝑚  between adjacent pulses are i.i.d. random variables which are exponentially distributed with the arrival rate 𝜆 . A healthy patient is characterized by the rate 𝜆 0 , while an unhealthy one is characterized by 𝜆 1 < 𝜆 0 . 𝑀  measurements of inter-pulse times are taken from a patient, and a healthy/unhealthy decision has to be made. However, the values of 𝜆 0  and 𝜆 1  are not known as they are in fact random. Specifically, each is assumed to be exponentially distributed, 𝜆 0  with mean value 𝜆 ¯ 0 , and 𝜆 1 with mean value 𝜆 ¯ 1 . With this model, the likelihood ratio is replaced by the Bayesian factor. The decision threshold is set to 𝜂 = 𝑃 0 𝑃 1 𝐶 𝑓 𝑎 𝐶 𝑚 𝑑 = 1 . 𝑀 = 10  observations are made on a patient, yielding the measured values 𝑦 1 , … 𝑦 𝑀 . If 𝜆 ¯ 0 = 1  and 𝜆 ¯ 1 = 𝜆 ¯ 0 / 4 , which of the following represents the Bayesian decision rule (numbers are rounded):