4,808 views
5 votes
5 votes
Assume that in a traffic junction, the cycle of traffic signal lights is 2 minutes of green(vehicle does not stop) and 3 minutes of red (vehicle stops). Consider the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time in minutes for the vehicle at the junction is _________

1 Answer

Best answer
3 votes
3 votes

Here in the span of $5$ minutes there is $2$ minute of $"no"$ waiting time and $3$ minute of waiting time that depends on the arrival,  it could take any value from $0-3$ minutes.

So I am assuming that starting $3$ minutes its RED and last $2$ min its GREEN.

$\therefore $ the function of waiting time is $\color{Blue }{3-x}$ $\{$ if a person arrive at time 0 it will wait for 3 minutes and soon and so forth.$\}$


Since its uniformly distributed expected waiting time will be :
$\Rightarrow $  $\Large \frac{1}{5-0}\int_{0}^{3}(3-x) \ dx$

$\Rightarrow $$\Large \frac{1}{5}[9-\frac{9}{2}]$

$\Rightarrow $$\Large \frac{9}{10}=\color{Red}{0.9}$

selected by

Related questions

33 votes
33 votes
4 answers
1
Arjun asked Feb 7, 2019
16,084 views
Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2 +6xY+3Y+6$ has only real roots is (rounded off to $1$ decimal...