Expected mass of meteorites in a day

Question

Small meteorites reach a collecting area as a Poisson process at rate $0.5$ per hour. Independently, each has an average mass of $2$ kg. Consider a full $24$ -hour day.

What is the expected total mass of meteorites collected in the day?

Accepted Answer

The day's total mass is a compound Poisson sum: a random number of meteorites, each of random mass. Its expectation is the expected number of meteorites times the average mass of each. The expected number of meteorites is E[N] = \lambda t = 0.5 	imes 24 = 12. Each averages 2 kg, so E[	ext{mass}] = E[N] 	imes E[	ext{mass per rock}] = 12 	imes 2 = 24 	ext{ kg}. Plainly: about 12 meteorites are expected, each about 2 kg, for roughly 24 kg total. Takeaway. Even with a low arrival rate, the expected total is just (expected count) times (average size): here 12 	imes 2 = 24 kg.

Expected mass of meteorites in a day

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