00:01
For this exercise, we are told that customers arrive at a certain restaurant according to a poisson distribution with an average rate of 2 .44 per minute.
00:14
And then we are asked for some probabilities for certain amounts of time elapsing between customer arrivals.
00:21
So let's define a random variable x as the time between customer arrivals.
00:26
Now, if customers are arriving according to a plosan distribution, then the time between arrivals is an exponential distribution with an average rate parameter, lambda, equal to the average arrival rate of the ploson distribution.
00:57
So this is 2 .44 per minute.
01:12
Now the cumulative distribution function of the exponential random variable is given by this formula.
01:34
For part a we want the probability that at least 10 minutes elapses between arrivals.
01:40
So this is the probability that x is greater than equal to 10.
01:45
This can be re -expressed as 1 minus, the probability that x is less than 10.
01:53
And so we can use the probability or the cumulative distribution function by substituting 10 for x as well as 2 .44 for lambda.
02:05
So we have 1 minus e to the negative.
02:12
2 .44 times 10.
02:18
Actually, it's supposed to be 1 minus all of this.
02:25
So that's just plus e to the minus 2 .44 times 10...