Consider one signal phase $($movement$)$ with $3$ seconds gap extension time in an actuated signal

system. Vehicle arrivals for this phase follow Poisson process at a rate of $600$ vehicles per hour.

This means that the time between vehicle arrivals follows the following exponential distribution:

$(>=)=$

$$

$$

Where $$ is the arrival flow and $$ is the time interval.

In one of the signal cycles, we observe $5$ successive extensions before the phase changes. What

is the probability of observing a headway that is less than $3$ seconds for the $5$ successive

extensions $(5$ times$)?$Consider one signal phase $($movement$)$ with $3$ seconds gap extension time in an actuated signal

system. Vehicle arrivals for this phase follow Poisson process at a rate of $600$ vehicles per hour.

This means that the time between vehicle arrivals follows the following exponential distribution:

$P(ht)=e^{-\frac{qt}{3600}}$

Where $q$ is the arrival flow and $t$ is the time interval.

In one of the signal cycles, we observe $5$ successive extensions before the phase changes. What

is the probability of observing a headway that is less than $3$ seconds for the $5$ successive

extensions $(5$ times$)?$

$($A$)0\mathrm{.}0075$

$($B$)0\mathrm{.}0094$

$($C$)0\mathrm{.}0081$

$($D$)0$