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A particular fast-food outlet is interested in the joint behavior of the random variable Y1, the total time between a customer’s arrival at the store and his leaving the service window, and let Y2, the time that the customer waits in line before reaching the service. Since Y1 contains the time a customer waits in line, we must have Y1 ≥  Y2. The relative frequency distribution of observed values of Y1 and Y2 can be modelled by the probability density function Find P(Y1 < 2, Y2 > 1). Find P(Y1 ≥ 2Y2). Find P( Y1 – Y2 ≥1). [Note Y1 -Y2 denote the time spent at the service window ] If a customer’s total waiting time service time is known to be more than 2 minutes, find the probability that the customer waited less than 1 minute to be served. Find E(Y1 – Y2). Find V(Y1 – Y2). Is it highly likely that a customer would spend more than 2 minutes at the service window? Find P( Y1 – Y2 < 0.5Y1)

A particular fast-food outlet is interested in the joint behavior of the random variable Y1, the total time between a customer’s arrival at the store and his leaving the service window, and let Y2, the time that the customer waits in line before reaching the service. Since Y1 contains the time a customer waits in line, we must have Y1 ≥  Y2. The relative frequency distribution of observed values of Y1 and Y2 can be modelled by the probability density function Find P(Y1 < 2, Y2 > 1). Find P(Y1 ≥ 2Y2). Find P( Y1 – Y2 ≥1). [Note Y1 -Y2 denote the time spent at the service window ] If a customer’s total waiting time service time is known to be more than 2 minutes, find the probability that the customer waited less than 1 minute to be served. Find E(Y1 – Y2). Find V(Y1 – Y2). Is it highly likely that a customer would spend more than 2 minutes at the service window? Find P( Y1 – Y2 < 0.5Y1)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 7CR
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A particular fast-food outlet is interested in the joint behavior of the random variable Y1, the total time between a customer’s arrival at the store and his leaving the service window, and let Y2, the time that the customer waits in line before reaching the service. Since Y1 contains the time a customer waits in line, we must have Y1 ≥  Y2. The relative frequency distribution of observed values of Y1 and Y2 can be modelled by the probability density function

  1. Find P(Y1 < 2, Y2 > 1).
  2. Find P(Y1 ≥ 2Y2).
  3. Find P( Y1 – Y2 ≥1). [Note Y1 -Y2 denote the time spent at the service window ]
  4. If a customer’s total waiting time service time is known to be more than 2 minutes, find the probability that the customer waited less than 1 minute to be served.
  5. Find E(Y1 – Y2).
  6. Find V(Y1 – Y2).
  7. Is it highly likely that a customer would spend more than 2 minutes at the service window?
  8. Find P( Y1 – Y2 < 0.5Y1)
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