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

Question

Dakota Ellison

Mathematics

24 March, 08:07

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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Brianna Dawson · Answer 1

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