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A commuter attempts to catch the 8:00 am train every morning although his arrival time at the station is a random variable that is uniformly dis- tributed between 7:55 am and 8:05 am. The train's departure time from the station is also a random variable that is uniformly distributed between 8:00 am and 8:10 am. a) Find the probability density function of the time interval between the commuter's arrival at station and the train's departure time. b) Find the probability that the commuter will catch the train. c) If the commuter gets delayed 3 minutes by a traffic jam, find the probability that the train will still be at the station.

A commuter attempts to catch the 8:00 am train every morning although his arrival time at the station is a random variable that is uniformly dis- tributed between 7:55 am and 8:05 am. The train's departure time from the station is also a random variable that is uniformly distributed between 8:00 am and 8:10 am. a) Find the probability density function of the time interval between the commuter's arrival at station and the train's departure time. b) Find the probability that the commuter will catch the train. c) If the commuter gets delayed 3 minutes by a traffic jam, find the probability that the train will still be at the station.

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 60CR
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A commuter attempts to catch the 8:00 am train every morning although his arrival time at the station is a random variable that is uniformly dis- tributed between 7:55 am and 8:05 am. The train's departure time from the station is also a random variable that is uniformly distributed between 8:00 am and 8:10 am. a) Find the probability density function of the time interval between the commuter's arrival at station and the train's departure time. b) Find the probability that the commuter will catch the train. c) If the commuter gets delayed 3 minutes by a traffic jam, find the probability that the train will still be at the station.
Transcribed Image Text:A commuter attempts to catch the 8:00 am train every morning although his arrival time at the station is a random variable that is uniformly dis- tributed between 7:55 am and 8:05 am. The train's departure time from the station is also a random variable that is uniformly distributed between 8:00 am and 8:10 am. a) Find the probability density function of the time interval between the commuter's arrival at station and the train's departure time. b) Find the probability that the commuter will catch the train. c) If the commuter gets delayed 3 minutes by a traffic jam, find the probability that the train will still be at the station.
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