00:01
Right, so we have ourselves a poisson random process.
00:04
The rate lambda is 30, customers an hour.
00:09
So we're going to find the probability that exactly eight customers arrive in the first 20 minutes.
00:15
So we're giving lambda is 30 customers an hour.
00:17
So for this one, but a, before i do that, the, just as a reminder, the poisson distribution formula is this, lambda to the x, e to the negative lambda, all over x factorial.
00:39
So here for a, we have lambda is 30, but we have to multiply it by time.
00:45
In this case, 20 minutes in terms of an hour is one third of an hour.
00:49
So in this case, our lambda is 10.
00:51
And what exactly 8? so in this case, x is 8.
00:56
So you get a p of 8 is.
00:58
And we just substituted in the 10 and the 8 into here.
01:02
So 10 to the 8th, e to then negative 10 all over, 8 factorial.
01:11
And we get 0 .1126.
01:18
It would be exactly 8 customers arrive in the first 20 minutes.
01:25
And exactly 22 arriving in the next 40 minutes.
01:28
So we already figured out the first 8.
01:30
So we're going to use this.
01:31
So basically what we're going to be doing is taking p of 8.
01:35
This is where lambda is 10.
01:38
And then we want the probability where lambda is something, 22.
01:48
But we need to throw out that lambda.
01:49
That lambda is, what's 30 times the t of 40 minutes? in terms of an hour is two -thirds, which gives us 20.
02:00
So this is the lambda is 20.
02:04
So we have this value, and now we'll do this over here in a separate color.
02:12
We have p of 22 is 20, is our land.
02:21
Lambda, right, that to the x, which is 22, e to negative 20, all over 22 factorial.
02:30
Don't do this by hand.
02:33
You want to do this with the calculator because that's going to make it a lot easier.
02:42
So we take this times that, and that's going to give us our value here.
02:49
So 0 .0767 times, actually, let me do this.
02:55
There's an order as i've written over here.
02:56
So we have 1 ,1126 times 0 .0767.
03:07
And we get 0086.
03:21
There's that...