The alternative way to travel from Seremban to Kuala Lumpur is by the KTM Seremban to Kuala Lumpur Sentral Commuter Train that operates many trips a day starting from the early morning until the late evening. Every trip takes 1 hour and 25 minutes. It is assumed that the train arrives at Kuala Lumpur Sentral uniformly between 0 and 110 minutes. i) Calculate the probability that the train takes between 40 and 90 minutes to arrive at Kuala Lumpur Sentral. ii) What is the average time taken to travel from KTM Seremban to Kuala Lumpur Sentral?
The alternative way to travel from Seremban to Kuala Lumpur is by the KTM Seremban to Kuala Lumpur Sentral Commuter Train that operates many trips a day starting from the early morning until the late evening. Every trip takes 1 hour and 25 minutes. It is assumed that the train arrives at Kuala Lumpur Sentral uniformly between 0 and 110 minutes. i) Calculate the probability that the train takes between 40 and 90 minutes to arrive at Kuala Lumpur Sentral. ii) What is the average time taken to travel from KTM Seremban to Kuala Lumpur Sentral?
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
Section13.1: Continuous Probability Models
Problem 28E
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a) The alternative way to travel from Seremban to Kuala Lumpur is by the KTM Seremban to
Kuala Lumpur Sentral Commuter Train that operates many trips a day starting from the
early morning until the late evening. Every trip takes 1 hour and 25 minutes. It is assumed
that the train arrives at Kuala Lumpur Sentral uniformly between 0 and 110 minutes.
i) Calculate the probability that the train takes between 40 and 90 minutes to arrive at
Kuala Lumpur Sentral.
ii) What is the average time taken to travel from KTM Seremban to Kuala Lumpur
Sentral?
Transcribed Image Text:b) A random variable Y has a probability density function defined as:
-y
1
f(y)=
0<y<∞ .
otherwise
i) Derive the moment generating function of Y.
ii) Find the mean and variance of Y using the moment generating function.
iii) Calculate the value of 0 if given P Y >
= e
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