Expected cargo delivered in a shift

Question

Trucks arrive at a depot as a Poisson process at rate $4$ per hour. Independently, each truck carries an average of $250$ kg of cargo. The shift lasts $10$ hours.

What is the expected total cargo delivered during the shift?

Accepted Answer

The total cargo is a compound Poisson sum: a random number of trucks, each with a random load. Its expectation is the expected number of trucks times the average load per truck. The expected number of trucks is E[N] = \lambda t = 4 	imes 10 = 40. Each carries 250 kg on average, so E[	ext{cargo}] = E[N] 	imes E[	ext{load}] = 40 	imes 250 = 10{,}000 	ext{ kg}. Simply put: about 40 trucks arrive, each with roughly 250 kg, for about 10{,}000 kg total. Takeaway. Expected throughput equals (expected number of carriers) times (average load each), a rule that works for cargo, revenue, or any ad…

Expected cargo delivered in a shift

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