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A warehouse has a capacity to hold four items. If the warehouse is neither full nor empty, the number of items in the warehouse changes whenever a new item is produced or an item 1 is sold. Suppose that the probability that the next event is “a new item is produced” is 2/3 and that the new event is a “sale” is 1/3.

0 1/3 2/3 0 0 0 1 1/3 0 2/3 0 0 2 0 1/3 0 2/3 0 3 0 0 1/3 0 2/3 4 0 0 0 1/3 2/3

Suppose there is currently one item in the warehouse. What is the expected time to reach 0 or 4?

math   Statistics-And-Probability   
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