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In 1950 an experiment was done observing the time gaps between successive cars on the Arroyo Seco Freeway. data show that the density function of these time gaps was given approximately by -0.124t f(t) = ae where t is the time in seconds and a is a constant. a. Find the constant a. a = b. Find the probability distribution function F(t). F(t) = c. Find the expected value (mean) and median time gap. Expected Value = Median = Recall : m is the median if F(m) = 0.5

In 1950 an experiment was done observing the time gaps between successive cars on the Arroyo Seco Freeway. data show that the density function of these time gaps was given approximately by -0.124t f(t) = ae where t is the time in seconds and a is a constant. a. Find the constant a. a = b. Find the probability distribution function F(t). F(t) = c. Find the expected value (mean) and median time gap. Expected Value = Median = Recall : m is the median if F(m) = 0.5

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
Section13.1: Continuous Probability Models
Problem 35E
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In 1950 an experiment was done observing the time gaps between successive cars on the Arroyo Seco Freeway. The data show that the density function of these time gaps was given approximately by -0.124t where f(t) = ae t is the time in seconds and a is a constant. a. Find the constant a. a b. Find the probability distribution function F(t). F(t) = c. Find the expected value (mean) and median time gap. Expected Value = Median: = Recall : m is the median if F(m) = 0.5
Transcribed Image Text:In 1950 an experiment was done observing the time gaps between successive cars on the Arroyo Seco Freeway. The data show that the density function of these time gaps was given approximately by -0.124t where f(t) = ae t is the time in seconds and a is a constant. a. Find the constant a. a b. Find the probability distribution function F(t). F(t) = c. Find the expected value (mean) and median time gap. Expected Value = Median: = Recall : m is the median if F(m) = 0.5
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