A Geiger counter beeps according to a Poisson process, with a rate of 5 beeps per minute.

(a). What is the probability that the observed average number of beeps per minute over the course of a day is between 4.9 and 5.1 ?

(b). What is the probability of 2 or more beeps during the next second?

(c). Given that there are exactly 3 beeps during the next minute, what is the probability that there was one during the first 20 seconds, one during the next 20 seconds, and one during the last 20 seconds?

(d) Suppose that there is a radioactive sample near the Geiger counter that is causing beeps at a rate of 4 per minute. The other beeps are from background radiation. What is the probability that, of the next 10 beeps, exactly three are from background radiation?

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A Geiger counter beeps according to a Poisson process with a rate of 5 beeps per minute a These are ... View the full answer