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12 November, 19:03

Suppose that each customer asks to sample a food item with probability 1/4, independently of all other customers. The service time for a customer who samples a food item is an exponential random variable with parameter 1/5. i. What is the expected number of minutes until you reach the front of the line

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  1. 12 November, 22:27
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    An approximately 2 minutes is expected to reach the front of the line

    Step-by-step explanation:

    Expected value of minutes =

    (1/4) ^ (1/5) + (1 - 1/4) ^ (1/5)

    = (1/4) ^0.2 + (3/4) ^0.2

    = 0.7579 + 0.9441

    = 1.702.

    ≈ 2 minutes
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