Trick or treaters arrive to your house according to a Poisson process with a constant rate parameter of 20 per hour. Suppose you begin sitting on your front porch, observing these arrivals, at some point in time. Suppose a trick or treater arrived 30 minutes ago, but there have been none since. What is the expected value of interarrival time (in minutes) from the previous trick or treater to the next one

The expected value of interarrival time (in minutes) from the previous trick or treater to the next one is 3 minutes.

Step-by-step explanation:

We have a Poisson process with a constant rate parameter of 20 arrival per hour.

This type of processes are memory-less, meaning that no matter how much time has passed form the last event, the probabilities of an arrival stay the same.

The mean interarrival time can be calculated as the inverse of the mean arrival for the Poisson process.

If the Poisson process has a rate of 20 arrivals per hour, the mean interarrival time is:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol