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rpois(1, 14) (Language R) is run repeatedly in order to create a bus schedule. A number...

rpois(1, 14) (Language R)

is run repeatedly in order to create a bus schedule. A number generated on each run is the

time, in minutes, between two buses. For example, if the generated numbers are 15, 20, 11, etc.

then there will be a bus at midnight, then at 12:15, 12:35, 12:46, etc. With a schedule

generated by the rpois(1, 14) code, what is the average wait time for a traveler arriving at the

bus stop, in minutes? (The 12:15, 12:35, 12:46 is just an example, the real schedule is not

known, it is only known that it was generated by the given code.) Please round to three

decimal places, if applicable.

math   Statistics-And-Probability   
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Answer #1

The numbers generated are having a Poisson distribution with lambda = 14

so the mean obtained will be close to 14

R code to do simulation for 100000 times

#empty vector to store schedule time values
schedule_time = c()
#Genrating and storing scheduled time
for(i in 1:100000){
time=rpois(1,14)
schedule_time[i]=time
}
mean(schedule_time)

-------------------------------------------------------------

mean obtained

>mean(schedule_time)
[1] 13.99995

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