Our faucet is broken and a plumber has been called. The arrival of the plumber is uniformly distributed between 1pm and 7pm. Independently of when the plumber arrives, the time it takes to fix the broken faucet is exponentially distributed with mean 30 min. What is the expectation of the time at which the plumber has fixed the faucet (take hours to be the unit of the problem, starting at 0=noon)?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Our faucet is broken and a plumber has been called. The arrival of the plumber is uniformly
distributed between 1pm and 7pm. Independently of when the plumber arrives, the time it
takes to fix the broken faucet is exponentially distributed with mean 30 min.
What is the expectation of the time at which the plumber has fixed the faucet (take hours
to be the unit of the problem, starting at 0=noon)?
Transcribed Image Text:Our faucet is broken and a plumber has been called. The arrival of the plumber is uniformly distributed between 1pm and 7pm. Independently of when the plumber arrives, the time it takes to fix the broken faucet is exponentially distributed with mean 30 min. What is the expectation of the time at which the plumber has fixed the faucet (take hours to be the unit of the problem, starting at 0=noon)?
What is the standard deviation of the time at which the plumber has fixed the faucet?
(same unit as explained above)
Give the answer up to two decimals.
Transcribed Image Text:What is the standard deviation of the time at which the plumber has fixed the faucet? (same unit as explained above) Give the answer up to two decimals.
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