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Chapter 5: Q. 5.13 (page 218)

At a certain bank, the amount of time that a customer spends being served by a teller is an exponential random variable with mean 5minutes. If there is a customer in service when you enter the bank, what is the probability that he or she will still be with the teller after an additional 4minutes?

Short Answer

Expert verified

The necessary probability of bank is around 0.45.

Step by step solution

01

Step :1   Random variables 

Establish Xas a variable quantity that represents the number of your time spent at the bank teller. We're given the knowledge that X~Expo鈦�(位)and EX=5, implying that 位=15. Assume there's a customer at the teller once we enter the bank. We are able to leverage the memoryless property of the exponential distribution, which states that we can reset time and observe from the beginning at any time. Assume there's a customer has only recently begun functioning at the teller. The likelihood that he will remain unmoved

02

Step :2 Substitution 

P(X>4)=1鈭�P(X鈮�4)=1鈭�1鈭�e鈭�15脳4=e鈭�45=0.45P(X>4)鈮�0.45

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