Question

2. The 46A bus leaves the terminus every 10 minutes exactly. For this reason, for any individual who arrives at a bus stop on the route, his minimum waiting time is 0 minutes and his maximum waiting time is 10 minutes, and between these two times, all possible waiting times are equally likely. Write down the probability density function for waiting times on the bus route and draw the distribution. What is the expected waiting time? What is the standard deviation of the waiting time?

Answer 1

As the waiting time is equally likely between the given times , it represents a Uniform distribution .

Let , T be the waiting time .

Then T~ Uni( 0 , 10)

So, pdf of T is given by :

  

0<t< 10 fr(t) = T 10

Here is the drawing of the distribution :

Distribution Plot Uniform, Lower-0, Upper-10 0.10 r 0.08 0.06 0.04 0.02 10 4

E T 0 r+1)10 10(r+1)0 100+1) 10(r 1)

So, E(T) = 100/20 = 5 min

E(T² ) = 100 /3

100 2 -52 V(T) = E(T*)-E2(T) = So,

So,

= 2.88 min SdT25