00:01
The scenario for this exercise is emergency 911 calls to a small municipality in idaho come in at a rate of one every three minutes.
00:12
And for part a, we're asked for the expected number of calls in one hour.
00:17
Now first, when we just have some phenomenon that's occurring randomly, such as emergency calls, and all we know about it is they're occurring at random and we have an average rate of occurrence, we can model the number in a given duration as a poisson random variable.
00:33
So we can model the number that occur in a certain period as a poisson with an average rate of one every three minutes, or one third per minute.
00:58
For part a, we want the expected number of calls in one hour.
01:06
So we're dealing with a time period of 60 minutes, expected number of calls.
01:12
This is equal to the average rate per minute times the number of minutes, about 20.
01:27
And then for b, we are asked for the probability of two calls in five minutes.
01:33
So now we're dealing with a time period of five minutes.
01:36
Now first, the probability function for the poisson random variable is given by this formula.
01:45
It's the mean number to the exponent x times e to the minus mean over x factorial.
01:51
X is any non -negative integer...