The amount of time a driver needs to react to a changing stoplight varies from driver to driver. The density function below roughly describes the probability distribution of this time, where x is given in seconds. f(x)= 0.8 e-0.8, if x > 0. a) Find the average reaction time. seconds. b) Consider Y = 5X +8 to be a modified reaction time. Find the expected value of Y. seconds.
The amount of time a driver needs to react to a changing stoplight varies from driver to driver. The density function below roughly describes the probability distribution of this time, where x is given in seconds. f(x)= 0.8 e-0.8, if x > 0. a) Find the average reaction time. seconds. b) Consider Y = 5X +8 to be a modified reaction time. Find the expected value of Y. seconds.
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![**Understanding Driver Reaction Times at Stoplights**
The amount of time a driver needs to react to a changing stoplight varies from driver to driver. The density function below roughly describes the probability distribution of this time, where \( x \) is given in seconds.
\[ f(x) = 0.8 \, e^{-0.8x}, \quad \text{if } x > 0. \]
### Tasks:
a) **Find the average reaction time.**
[Answer box] seconds.
b) **Consider \( Y = 5X + 8 \) to be a modified reaction time. Find the expected value of \( Y \).**
[Answer box] seconds.
This exercise involves calculating the average (expected) reaction time of drivers and finding the expected value of a modified reaction time using a given mathematical model.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80864b91-d3a3-4910-ac0e-8d4cb607fd82%2Fb22ad4c6-34ef-4b83-9531-e6b4a43bd383%2Fcb8fhfk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Driver Reaction Times at Stoplights**
The amount of time a driver needs to react to a changing stoplight varies from driver to driver. The density function below roughly describes the probability distribution of this time, where \( x \) is given in seconds.
\[ f(x) = 0.8 \, e^{-0.8x}, \quad \text{if } x > 0. \]
### Tasks:
a) **Find the average reaction time.**
[Answer box] seconds.
b) **Consider \( Y = 5X + 8 \) to be a modified reaction time. Find the expected value of \( Y \).**
[Answer box] seconds.
This exercise involves calculating the average (expected) reaction time of drivers and finding the expected value of a modified reaction time using a given mathematical model.
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