"Time Headway" in Traffic Flow Is the Elapsed Time Between $f ( x ) = \left\{ \begin{array} { c l } .15 e ^ { - 1 ( x - 5 ) } & x \geq 5 \\0 & \text { otherwise }\end{array} \right.$

question 6

Essay

"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow. The following pdf of X is $f ( x ) = \left\{ \begin{array} { c l } .15 e ^ { - 1 ( x - 5 ) } & x \geq 5 \\0 & \text { otherwise }\end{array} \right.$ What is the probability that the time headway is
a. At most 6 seconds?
b. At least 6 seconds?
c. At most 5 seconds?
d. Between 5 and 6 seconds?

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