"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?

Question

"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?

Quizplus · Accepted Answer

The Answer of "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?

"Time Headway" in Traffic Flow Is the Elapsed Time Between f(x)={.15e−1(x−5)x≥50 otherwise f ( x ) = \left\{ \begin{array} { c l } .15 e ^ { - 1 ( x - 5 ) } & x \geq 5 \\0 & \text { otherwise }\end{array} \right.f(x)={.15e−1(x−5)0​x≥5 otherwise ​

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