We know that average number of planes landing at particular airport during an hour is 36.
a) what is the mean time for waiting for the first landing during an hour?
b) find probability of waiting more than 1/2 hour to see the first landing?
I assumed this is Poisson distribution as Exponential is memoryless (each minute would have independent probability, am I right?)
But to be honest I don't really know what to do next.
I wrote down the data from the task:
$$\lambda = 36$$
And I'm stuck. Looking more for tips how to solve this task, not full solution.
Thank you for help in advance.
Best Answer
For part (a), you are given that on average $36$ planes are observed every hour. In this case, on average, how many hours does it take to observe a plane? What is this in minutes?
For (b), if $36$ planes land in an hour, how many planes land in half an hour on average? Then what is the probability of seeing no planes in the first half hour?